document.write( "Question 213791This question is from textbook College Algebra
\n" ); document.write( ": (6/2x-2)-(1/x+1)=(2/2x+2)+1 \n" ); document.write( "

Algebra.Com's Answer #161507 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
use y=1/x and get: \r
\n" ); document.write( "\n" ); document.write( " $\"%286%2F2x-2%29-%281%2Fx%2B1%29=%282%2F2x%2B2%29%2B1\"$ or $\"%286%2F2%2Ay-2%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1\"$ \r
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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: y=6.
Graphical form: Equation $\"%286%2F2%2Ay-2%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1\"$ was fully solved.
Text form: (6/2*y-2)-(y+1)=(2/2*y+2)+1 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+%286%2F2%2Ay-2%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1+%29\"$
For tutors: simplify_cartoon( (6/2*y-2)-(y+1)=(2/2*y+2)+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 $\"highlight_red%28+%286%2F2%2Ay-2%29+%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+6%2F2%2Ay+%29\"$ , $\"highlight_red%28+-2+%29\"$
It becomes

.
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Look at $\"6%2F2%2Ay-2-highlight_red%28+%28y%2B1%29+%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+-y+%29\"$ , $\"highlight_red%28+-1+%29\"$
It becomes $\"6%2F2%2Ay-2-highlight_green%28+y+%29-highlight_green%28+1+%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"highlight_red%28+6+%29%2Fhighlight_red%28+2+%29%2Ay-2-y-1=%282%2F2%2Ay%2B2%29%2B1\"$ .
Factors 6 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes $\"highlight_green%28+3+%29%2Fhighlight_green%28+1+%29%2Ay-2-y-1=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"3%2F1%2Ay-highlight_red%28+2+%29-y-highlight_red%28+1+%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
Added fractions or integers together
It becomes $\"3%2F1%2Ay%2Bhighlight_green%28+-3+%29-y=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"3%2F1%2Ay%2Bhighlight_red%28+-3+%29-y=%282%2F2%2Ay%2B2%29%2B1\"$ .
Moved $\"-3\"$ to the right of expression
It becomes $\"3%2F1%2Ay-y%2Bhighlight_green%28+-3+%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"3%2F1%2Ay-y%2Bhighlight_red%28+-3+%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
Removed extra sign in front of $\"-3\"$
It becomes $\"3%2F1%2Ay-y-highlight_green%28+3+%29=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"3%2Fhighlight_red%28+1+%29%2Ay-y-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1%2F1+%29\"$
It becomes $\"3%2Ay-y-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"highlight_red%28+3%2Ay+%29-highlight_red%28+y+%29-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
Eliminated similar terms $\"highlight_red%28+3%2Ay+%29\"$ , $\"highlight_red%28+-y+%29\"$ replacing them with $\"highlight_green%28+%283-1%29%2Ay+%29\"$
It becomes $\"highlight_green%28+%283-1%29%2Ay+%29-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"%28highlight_red%28+3+%29-highlight_red%28+1+%29%29%2Ay-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+2+%29%29%2Ay-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+2+%29%29%2Ay+%29-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"highlight_green%28+2+%29%2Ay-3=%282%2F2%2Ay%2B2%29%2B1\"$ .
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Look at $\"2%2Ay-3=highlight_red%28+%282%2F2%2Ay%2B2%29+%29%2B1\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+2%2F2%2Ay+%29\"$ , $\"highlight_red%28+2+%29\"$
It becomes $\"2%2Ay-3=highlight_green%28+2%2F2%2Ay+%29%2Bhighlight_green%28+2+%29%2B1\"$ .
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Look at $\"2%2Ay-3=highlight_red%28+2+%29%2Fhighlight_red%28+2+%29%2Ay%2B2%2B1\"$ .
Factors 2 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes $\"2%2Ay-3=highlight_green%28+1+%29%2Fhighlight_green%28+1+%29%2Ay%2B2%2B1\"$ .
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Look at $\"2%2Ay-3=1%2F1%2Ay%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+1+%29\"$ .
Added fractions or integers together
It becomes $\"2%2Ay-3=1%2F1%2Ay%2Bhighlight_green%28+3+%29\"$ .
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Look at $\"2%2Ay-3=highlight_red%28+1+%29%2Fhighlight_red%28+1+%29%2Ay%2B3\"$ .
Reduce similar several occurrences of $\"highlight_red%28+1+%29\"$ to
It becomes $\"2%2Ay-3=y%2B3\"$ .
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Look at $\"2%2Ay-3=highlight_red%28+y%2B3+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-y+%29\"$ , $\"highlight_green%28+-3+%29\"$
It becomes $\"2%2Ay-3-highlight_green%28+y+%29-highlight_green%28+3+%29=0\"$ .
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Look at $\"2%2Ay-highlight_red%28+3+%29-y-highlight_red%28+3+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2Ay%2Bhighlight_green%28+-6+%29-y=0\"$ .
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Look at $\"2%2Ay%2Bhighlight_red%28+-6+%29-y=0\"$ .
Moved $\"-6\"$ to the right of expression
It becomes $\"2%2Ay-y%2Bhighlight_green%28+-6+%29=0\"$ .
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Look at $\"2%2Ay-y%2Bhighlight_red%28+-6+%29=0\"$ .
Removed extra sign in front of $\"-6\"$
It becomes $\"2%2Ay-y-highlight_green%28+6+%29=0\"$ .
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Look at $\"highlight_red%28+2%2Ay+%29-highlight_red%28+y+%29-6=0\"$ .
Eliminated similar terms $\"highlight_red%28+2%2Ay+%29\"$ , $\"highlight_red%28+-y+%29\"$ replacing them with $\"highlight_green%28+%282-1%29%2Ay+%29\"$
It becomes $\"highlight_green%28+%282-1%29%2Ay+%29-6=0\"$ .
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Look at $\"highlight_red%28+%282-1%29+%29%2Ay-6=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+%282-1%29+%29\"$
It becomes $\"y-6=0\"$ .
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Look at $\"highlight_red%28+y-6+%29=0\"$ .
Solved linear equation $\"highlight_red%28+y-6=0+%29\"$ equivalent to y-6 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: y=6.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "since y = 6, then $\"x+=+1%2Fy+=+1%2F6\"$ \n" ); document.write( "

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