document.write( "Question 27359: -3(x+5)=3(x-1)\r
\n" ); document.write( "\n" ); document.write( "6-b=5b+30\r
\n" ); document.write( "\n" ); document.write( "5y-2y=3y+2\r
\n" ); document.write( "\n" ); document.write( "2(7+3t)=-t\r
\n" ); document.write( "\n" ); document.write( "3(a+1)-5=3a-2 \n" ); document.write( "

Algebra.Com's Answer #14848 by Alwayscheerful(414) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"-3%28x%2B5%29=3%28x-1%29\"$
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: x=-2.
Graphical form: Equation $\"-3%2A%28x%2B5%29=3%2A%28x-1%29\"$ was fully solved.
Text form: -3*(x+5)=3*(x-1) simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+-3%2A%28x%2B5%29=3%2A%28x-1%29+%29\"$
For tutors: simplify_cartoon( -3*(x+5)=3*(x-1) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"-3%2A%28x%2B5%29=highlight_red%28+3%2A%28x-1%29+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2A%28x-1%29+%29\"$
It becomes $\"-3%2A%28x%2B5%29-highlight_green%28+3%2A%28x-1%29+%29=0\"$ .
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Look at $\"-highlight_red%28+3%2A%28x%2B5%29+%29-3%2A%28x-1%29=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28x%2B5%29\"$
It becomes $\"-highlight_green%28+3%2Ax+%29-highlight_green%28+3%2A5+%29-3%2A%28x-1%29=0\"$ .
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Look at $\"-3%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+5+%29-3%2A%28x-1%29=0\"$ .
Multiplied numerator integers
It becomes $\"-3%2Ax-highlight_green%28+15+%29-3%2A%28x-1%29=0\"$ .
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Look at $\"-3%2Ax-highlight_red%28+15+%29-3%2A%28x-1%29=0\"$ .
Moved $\"-15\"$ to the right of expression
It becomes $\"-3%2Ax-3%2A%28x-1%29-highlight_green%28+15+%29=0\"$ .
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Look at $\"-3%2Ax-highlight_red%28+3%2A%28x-1%29+%29-15=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28x-1%29\"$
It becomes $\"-3%2Ax-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A1+%29-15=0\"$ .
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Look at $\"-3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-15=0\"$ .
Multiplied numerator integers
It becomes $\"-3%2Ax-3%2Ax%2Bhighlight_green%28+3+%29-15=0\"$ .
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Look at $\"-3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29-highlight_red%28+15+%29=0\"$ .
Added fractions or integers together
It becomes $\"-3%2Ax-3%2Ax%2Bhighlight_green%28+-12+%29=0\"$ .
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Look at $\"-3%2Ax-3%2Ax%2Bhighlight_red%28+-12+%29=0\"$ .
Removed extra sign in front of $\"-12\"$
It becomes $\"-3%2Ax-3%2Ax-highlight_green%28+12+%29=0\"$ .
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Look at $\"-highlight_red%28+3%2Ax+%29-highlight_red%28+3%2Ax+%29-12=0\"$ .
Eliminated similar terms $\"highlight_red%28+-3%2Ax+%29\"$ , $\"highlight_red%28+-3%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-3-3%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%28-3-3%29%2Ax+%29-12=0\"$ .
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Look at $\"%28-highlight_red%28+3+%29-highlight_red%28+3+%29%29%2Ax-12=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-6+%29%29%2Ax-12=0\"$ .
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Look at $\"%28highlight_red%28+-6+%29%29%2Ax-12=0\"$ .
Removed extra sign in front of $\"-6\"$
It becomes $\"%28-highlight_green%28+6+%29%29%2Ax-12=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+6+%29%29%2Ax+%29-12=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+6+%29\"$
It becomes $\"-highlight_green%28+6+%29%2Ax-12=0\"$ .
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Look at $\"highlight_red%28+-6%2Ax-12+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-6%2Ax-12=0+%29\"$ equivalent to -6*x-12 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=-2.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( " $\"6-b=5b%2B30\"$
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: b=-4.
Graphical form: Equation $\"6-b=5b%2B30\"$ was fully solved.
Text form: 6-b=5b+30 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+6-b=5b%2B30+%29\"$
For tutors: simplify_cartoon( 6-b=5b+30 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+6+%29-b=5b%2B30\"$ .
Moved $\"6\"$ to the right of expression
It becomes $\"-b%2Bhighlight_green%28+6+%29=5b%2B30\"$ .
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Look at $\"-b%2B6=highlight_red%28+5%2Ab%2B30+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-5%2Ab+%29\"$ , $\"highlight_green%28+-30+%29\"$
It becomes $\"-b%2B6-highlight_green%28+5%2Ab+%29-highlight_green%28+30+%29=0\"$ .
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Look at $\"-b%2Bhighlight_red%28+6+%29-5%2Ab-highlight_red%28+30+%29=0\"$ .
Added fractions or integers together
It becomes $\"-b%2Bhighlight_green%28+-24+%29-5%2Ab=0\"$ .
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Look at $\"-b%2Bhighlight_red%28+-24+%29-5%2Ab=0\"$ .
Moved $\"-24\"$ to the right of expression
It becomes $\"-b-5%2Ab%2Bhighlight_green%28+-24+%29=0\"$ .
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Look at $\"-b-5%2Ab%2Bhighlight_red%28+-24+%29=0\"$ .
Removed extra sign in front of $\"-24\"$
It becomes $\"-b-5%2Ab-highlight_green%28+24+%29=0\"$ .
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Look at $\"-highlight_red%28+b+%29-highlight_red%28+5%2Ab+%29-24=0\"$ .
Eliminated similar terms $\"highlight_red%28+-b+%29\"$ , $\"highlight_red%28+-5%2Ab+%29\"$ replacing them with $\"highlight_green%28+%28-1-5%29%2Ab+%29\"$
It becomes $\"highlight_green%28+%28-1-5%29%2Ab+%29-24=0\"$ .
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Look at $\"%28-highlight_red%28+1+%29-highlight_red%28+5+%29%29%2Ab-24=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-6+%29%29%2Ab-24=0\"$ .
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Look at $\"%28highlight_red%28+-6+%29%29%2Ab-24=0\"$ .
Removed extra sign in front of $\"-6\"$
It becomes $\"%28-highlight_green%28+6+%29%29%2Ab-24=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+6+%29%29%2Ab+%29-24=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+6+%29\"$
It becomes $\"-highlight_green%28+6+%29%2Ab-24=0\"$ .
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Look at $\"highlight_red%28+-6%2Ab-24+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-6%2Ab-24=0+%29\"$ equivalent to -6*b-24 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: b=-4.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( " $\"5y-2y=3y%2B2\"$
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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Graphical form: $\"5y-2y=3y%2B2\"$ simplifies to $\"-2=0\"$
Text form: 5y-2y=3y+2 simplifies to -2=0
Cartoon (animation) form: $\"simplify_cartoon%28+5y-2y=3y%2B2+%29\"$
For tutors: simplify_cartoon( 5y-2y=3y+2 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+5%2Ay+%29-highlight_red%28+2%2Ay+%29=3y%2B2\"$ .
Eliminated similar terms $\"highlight_red%28+5%2Ay+%29\"$ , $\"highlight_red%28+-2%2Ay+%29\"$ replacing them with $\"highlight_green%28+%285-2%29%2Ay+%29\"$
It becomes $\"highlight_green%28+%285-2%29%2Ay+%29=3y%2B2\"$ .
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Look at $\"%28highlight_red%28+5+%29-highlight_red%28+2+%29%29%2Ay=3y%2B2\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+3+%29%29%2Ay=3y%2B2\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+3+%29%29%2Ay+%29=3y%2B2\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+3+%29\"$
It becomes $\"highlight_green%28+3+%29%2Ay=3y%2B2\"$ .
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Look at $\"3%2Ay=highlight_red%28+3%2Ay%2B2+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2Ay+%29\"$ , $\"highlight_green%28+-2+%29\"$
It becomes $\"3%2Ay-highlight_green%28+3%2Ay+%29-highlight_green%28+2+%29=0\"$ .
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Look at $\"highlight_red%28+3%2Ay+%29-highlight_red%28+3%2Ay+%29-2=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2Ay+%29\"$ , $\"highlight_red%28+-3%2Ay+%29\"$ replacing them with $\"highlight_green%28+%283-3%29%2Ay+%29\"$
It becomes $\"highlight_green%28+%283-3%29%2Ay+%29-2=0\"$ .
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Look at $\"highlight_red%28+%283-3%29%2Ay+%29-2=0\"$ .
Since $\"highlight_red%28+%283-3%29%2Ay+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"0-2=0\"$ .
Added fractions or integers together
It becomes $\"0-2=0\"$ .
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Look at $\"highlight_red%28+0+%29-2=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"-2=0\"$ .
Result: $\"-2=0\"$
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Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( " $\"2%287%2B3t%29=-t\"$
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: t=-2.
Graphical form: Equation $\"2%2A%287%2B3t%29=-t\"$ was fully solved.
Text form: 2*(7+3t)=-t simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+2%2A%287%2B3t%29=-t+%29\"$
For tutors: simplify_cartoon( 2*(7+3t)=-t )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"2%2A%28highlight_red%28+7+%29%2B3%2At%29=-t\"$ .
Moved $\"7\"$ to the right of expression
It becomes $\"2%2A%283%2At%2Bhighlight_green%28+7+%29%29=-t\"$ .
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Look at $\"2%2A%283%2At%2B7%29=highlight_red%28+-t+%29\"$ .
Moved these terms to the left $\"highlight_green%28+t+%29\"$
It becomes $\"2%2A%283%2At%2B7%29%2Bhighlight_green%28+t+%29=0\"$ .
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Look at $\"highlight_red%28+2%2A%283%2At%2B7%29+%29%2Bt=0\"$ .
Expanded term $\"2\"$ by using associative property on $\"%283%2At%2B7%29\"$
It becomes $\"highlight_green%28+2%2A3%2At+%29%2Bhighlight_green%28+2%2A7+%29%2Bt=0\"$ .
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Look at $\"highlight_red%28+2+%29%2Ahighlight_red%28+3+%29%2At%2B2%2A7%2Bt=0\"$ .
Multiplied numerator integers
It becomes $\"highlight_green%28+6+%29%2At%2B2%2A7%2Bt=0\"$ .
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Look at $\"6%2At%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+7+%29%2Bt=0\"$ .
Multiplied numerator integers
It becomes $\"6%2At%2Bhighlight_green%28+14+%29%2Bt=0\"$ .
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Look at $\"6%2At%2Bhighlight_red%28+14+%29%2Bt=0\"$ .
Moved $\"14\"$ to the right of expression
It becomes $\"6%2At%2Bt%2Bhighlight_green%28+14+%29=0\"$ .
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Look at $\"highlight_red%28+6%2At+%29%2Bhighlight_red%28+t+%29%2B14=0\"$ .
Eliminated similar terms $\"highlight_red%28+6%2At+%29\"$ , $\"highlight_red%28+t+%29\"$ replacing them with $\"highlight_green%28+%286%2B1%29%2At+%29\"$
It becomes $\"highlight_green%28+%286%2B1%29%2At+%29%2B14=0\"$ .
\n" ); document.write( "

Look at $\"%28highlight_red%28+6+%29%2Bhighlight_red%28+1+%29%29%2At%2B14=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+7+%29%29%2At%2B14=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+%28highlight_red%28+7+%29%29%2At+%29%2B14=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$
It becomes $\"highlight_green%28+7+%29%2At%2B14=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+7%2At%2B14+%29=0\"$ .
Solved linear equation $\"highlight_red%28+7%2At%2B14=0+%29\"$ equivalent to 7*t+14 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: t=-2.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( " $\"3%28a%2B1%29-5=3a-2\"$
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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Graphical form: Equation $\"3%2A%28a%2B1%29-5=3a-2\"$ was fully solved.
Text form: 3*(a+1)-5=3a-2 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+3%2A%28a%2B1%29-5=3a-2+%29\"$
For tutors: simplify_cartoon( 3*(a+1)-5=3a-2 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"3%2A%28a%2B1%29-5=highlight_red%28+3%2Aa-2+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2Aa+%29\"$ , $\"highlight_green%28+2+%29\"$
It becomes $\"3%2A%28a%2B1%29-5-highlight_green%28+3%2Aa+%29%2Bhighlight_green%28+2+%29=0\"$ .
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Look at $\"3%2A%28a%2B1%29-highlight_red%28+5+%29-3%2Aa%2Bhighlight_red%28+2+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2A%28a%2B1%29%2Bhighlight_green%28+-3+%29-3%2Aa=0\"$ .
\n" ); document.write( "

Look at $\"3%2A%28a%2B1%29%2Bhighlight_red%28+-3+%29-3%2Aa=0\"$ .
Moved $\"-3\"$ to the right of expression
It becomes $\"3%2A%28a%2B1%29-3%2Aa%2Bhighlight_green%28+-3+%29=0\"$ .
\n" ); document.write( "

Look at $\"3%2A%28a%2B1%29-3%2Aa%2Bhighlight_red%28+-3+%29=0\"$ .
Removed extra sign in front of $\"-3\"$
It becomes $\"3%2A%28a%2B1%29-3%2Aa-highlight_green%28+3+%29=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+3%2A%28a%2B1%29+%29-3%2Aa-3=0\"$ .
Expanded term $\"3\"$ by using associative property on $\"%28a%2B1%29\"$
It becomes $\"highlight_green%28+3%2Aa+%29%2Bhighlight_green%28+3%2A1+%29-3%2Aa-3=0\"$ .
\n" ); document.write( "

Look at $\"3%2Aa%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-3%2Aa-3=0\"$ .
Multiplied numerator integers
It becomes $\"3%2Aa%2Bhighlight_green%28+3+%29-3%2Aa-3=0\"$ .
\n" ); document.write( "

Look at $\"3%2Aa%2Bhighlight_red%28+3+%29-3%2Aa-highlight_red%28+3+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Aa%2Bhighlight_green%28+0+%29-3%2Aa=0\"$ .
\n" ); document.write( "

Look at $\"3%2Aa%2Bhighlight_red%28+0+%29-3%2Aa=0\"$ .
Moved $\"0\"$ to the right of expression
It becomes $\"3%2Aa-3%2Aa%2Bhighlight_green%28+0+%29=0\"$ .
\n" ); document.write( "

Look at $\"3%2Aa-3%2Aa%2Bhighlight_red%28+0+%29=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"3%2Aa-3%2Aa=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+3%2Aa+%29-highlight_red%28+3%2Aa+%29=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2Aa+%29\"$ , $\"highlight_red%28+-3%2Aa+%29\"$ replacing them with $\"highlight_green%28+%283-3%29%2Aa+%29\"$
It becomes $\"highlight_green%28+%283-3%29%2Aa+%29=0\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+%283-3%29%2Aa+%29=0\"$ .
Since $\"highlight_red%28+%283-3%29%2Aa+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"0=0\"$ .
Added fractions or integers together
It becomes $\"0=0\"$ .
Result: $\"0=0\"$
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Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Next time, please separate your questions. Thanks. :)
\n" ); document.write( "Hope this helps! \n" ); document.write( "

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