document.write( "Question 5835: We are doing Jacob's Algebra at home.
\n" ); document.write( "We are on Lesson 3 in Chapter 15
\n" ); document.write( "Set III Question 9 c
\n" ); document.write( "Here is what we have tried for days!
\n" ); document.write( "2x/x+5 - 3/x-2 = 1
\n" ); document.write( "First we multiplied both sides by (x+5)(x-2) to get
\n" ); document.write( "2x^2-4x-3x+15=(x+5) (x-2)
\n" ); document.write( "2x^2-7x+15 = x^2=5x-2x-10
\n" ); document.write( "x^2-10x+25=0
\n" ); document.write( "When we did the quadratic formula to get the answer we got the answer of just 5
\n" ); document.write( "but the answer in the book is
\n" ); document.write( "10.48 and -.48
\n" ); document.write( "So then we tried
\n" ); document.write( "multiplying each side by (x^2 +10)
\n" ); document.write( "(we weren't sure if we should maybe do (x^2 - 10), which could also work)
\n" ); document.write( "and we got these answers 4.52 and -5.52
\n" ); document.write( "which are also wrong!
\n" ); document.write( "Please let us know what to multiply by to get the right answer!
\n" ); document.write( "Thanks!
\n" ); document.write( "We will be checking all the time for your response! Thanks so much!
\n" ); document.write( "Julie Cochran
\n" ); document.write( "julie-cochran@earthlink.net \n" ); document.write( "

Algebra.Com's Answer #3009 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
great job trying!\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: x=10.4772255750517,x=-0.477225575051661.
Graphical form: Equation $\"2x%2A%28x-2%29-3%2A%28x%2B5%29=%28x-2%29%2A%28x%2B5%29\"$ was fully solved.
Text form: 2x*(x-2)-3*(x+5)=(x-2)*(x+5) simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+2x%2A%28x-2%29-3%2A%28x%2B5%29=%28x-2%29%2A%28x%2B5%29+%29\"$
For tutors: simplify_cartoon( 2x*(x-2)-3*(x+5)=(x-2)*(x+5) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"2%2Ax%2A%28x-2%29-3%2A%28x%2B5%29=highlight_red%28+%28x-2%29%2A%28x%2B5%29+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-%28x-2%29%2A%28x%2B5%29+%29\"$
It becomes $\"2%2Ax%2A%28x-2%29-3%2A%28x%2B5%29-highlight_green%28+%28x-2%29%2A%28x%2B5%29+%29=0\"$ .
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Look at $\"highlight_red%28+2%2Ax%2A%28x-2%29+%29-3%2A%28x%2B5%29-%28x-2%29%2A%28x%2B5%29=0\"$ .
Expanded term $\"2%2Ax\"$ by using associative property on $\"%28x-2%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"2%2Ax%2Ax-highlight_green%28+4+%29%2Ax-3%2A%28x%2B5%29-%28x-2%29%2A%28x%2B5%29=0\"$ .
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Look at

.
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"2%2Ahighlight_green%28+x%5E2+%29-4%2Ax-3%2A%28x%2B5%29-%28x-2%29%2A%28x%2B5%29=0\"$ .
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Look at $\"2%2Ax%5E2-4%2Ax-highlight_red%28+3%2A%28x%2B5%29+%29-%28x-2%29%2A%28x%2B5%29=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28x%2B5%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"2%2Ax%5E2-4%2Ax-3%2Ax-highlight_green%28+15+%29-%28x-2%29%2A%28x%2B5%29=0\"$ .
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Look at $\"2%2Ax%5E2-4%2Ax-3%2Ax-highlight_red%28+15+%29-%28x-2%29%2A%28x%2B5%29=0\"$ .
Moved $\"-15\"$ to the right of expression
It becomes $\"2%2Ax%5E2-4%2Ax-3%2Ax-%28x-2%29%2A%28x%2B5%29-highlight_green%28+15+%29=0\"$ .
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Look at $\"2%2Ax%5E2-highlight_red%28+4%2Ax+%29-highlight_red%28+3%2Ax+%29-%28x-2%29%2A%28x%2B5%29-15=0\"$ .
Eliminated similar terms $\"highlight_red%28+-4%2Ax+%29\"$ , $\"highlight_red%28+-3%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-4-3%29%2Ax+%29\"$
It becomes $\"2%2Ax%5E2%2Bhighlight_green%28+%28-4-3%29%2Ax+%29-%28x-2%29%2A%28x%2B5%29-15=0\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"2%2Ax%5E2%2B%28highlight_green%28+-7+%29%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0\"$ .
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Look at $\"2%2Ax%5E2%2B%28highlight_red%28+-7+%29%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0\"$ .
Removed extra sign in front of $\"-7\"$
It becomes $\"2%2Ax%5E2%2B%28-highlight_green%28+7+%29%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0\"$ .
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Look at

.
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$
It becomes $\"2%2Ax%5E2-highlight_green%28+7+%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0\"$ .
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Look at $\"2%2Ax%5E2-7%2Ax-highlight_red%28+%28x-2%29%2A%28x%2B5%29+%29-15=0\"$ .
Expanded term $\"-%28x%2B5%29\"$ by using associative property on $\"%28x-2%29\"$
It becomes

.
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Look at $\"2%2Ax%5E2-7%2Ax-highlight_red%28+%28x%2B5%29%2Ax+%29%2B%28x%2B5%29%2A2-15=0\"$ .
Expanded term $\"-x\"$ by using associative property on $\"%28x%2B5%29\"$
It becomes

.
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Look at $\"2%2Ax%5E2-7%2Ax-highlight_red%28+x+%29%2Ahighlight_red%28+x+%29-x%2A5%2B%28x%2B5%29%2A2-15=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"2%2Ax%5E2-7%2Ax-highlight_green%28+x%5E2+%29-x%2A5%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at $\"highlight_red%28+2%2Ax%5E2+%29-7%2Ax-highlight_red%28+x%5E2+%29-x%2A5%2B%28x%2B5%29%2A2-15=0\"$ .
Eliminated similar terms $\"highlight_red%28+2%2Ax%5E2+%29\"$ , $\"highlight_red%28+-x%5E2+%29\"$ replacing them with $\"highlight_green%28+%282-1%29%2Ax%5E2+%29\"$
It becomes $\"highlight_green%28+%282-1%29%2Ax%5E2+%29-7%2Ax-x%2A5%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+-7%2Ax+%29\"$ , $\"highlight_red%28+-x%2A5+%29\"$ replacing them with $\"highlight_green%28+%28-7-5%29%2Ax+%29\"$
It becomes $\"%282-1%29%2Ax%5E2%2Bhighlight_green%28+%28-7-5%29%2Ax+%29%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at $\"highlight_red%28+%282-1%29+%29%2Ax%5E2%2B%28-7-5%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+%282-1%29+%29\"$
It becomes $\"x%5E2%2B%28-7-5%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at $\"x%5E2%2B%28-highlight_red%28+7+%29-highlight_red%28+5+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
Added fractions or integers together
It becomes $\"x%5E2%2B%28highlight_green%28+-12+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at $\"x%5E2%2B%28highlight_red%28+-12+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
Removed extra sign in front of $\"-12\"$
It becomes $\"x%5E2%2B%28-highlight_green%28+12+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at $\"x%5E2%2Bhighlight_red%28+%28-highlight_red%28+12+%29%29%2Ax+%29%2B%28x%2B5%29%2A2-15=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+12+%29\"$
It becomes $\"x%5E2-highlight_green%28+12+%29%2Ax%2B%28x%2B5%29%2A2-15=0\"$ .
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Look at $\"x%5E2-12%2Ax%2Bhighlight_red%28+%28x%2B5%29%2A2+%29-15=0\"$ .
Expanded term $\"2\"$ by using associative property on $\"%28x%2B5%29\"$
It becomes $\"x%5E2-12%2Ax%2Bhighlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A5+%29-15=0\"$ .
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Look at $\"x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+5+%29-15=0\"$ .
Multiplied numerator integers
It becomes $\"x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_green%28+10+%29-15=0\"$ .
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Look at $\"x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_red%28+10+%29-highlight_red%28+15+%29=0\"$ .
Added fractions or integers together
It becomes $\"x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_green%28+-5+%29=0\"$ .
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Look at $\"x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_red%28+-5+%29=0\"$ .
Removed extra sign in front of $\"-5\"$
It becomes $\"x%5E2-12%2Ax%2B2%2Ax-highlight_green%28+5+%29=0\"$ .
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Look at $\"x%5E2-highlight_red%28+12%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29-5=0\"$ .
Eliminated similar terms $\"highlight_red%28+-12%2Ax+%29\"$ , $\"highlight_red%28+2%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-12%2B2%29%2Ax+%29\"$
It becomes $\"x%5E2%2Bhighlight_green%28+%28-12%2B2%29%2Ax+%29-5=0\"$ .
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Look at $\"x%5E2%2B%28-highlight_red%28+12+%29%2Bhighlight_red%28+2+%29%29%2Ax-5=0\"$ .
Added fractions or integers together
It becomes $\"x%5E2%2B%28highlight_green%28+-10+%29%29%2Ax-5=0\"$ .
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Look at $\"x%5E2%2B%28highlight_red%28+-10+%29%29%2Ax-5=0\"$ .
Removed extra sign in front of $\"-10\"$
It becomes $\"x%5E2%2B%28-highlight_green%28+10+%29%29%2Ax-5=0\"$ .
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Look at $\"x%5E2%2Bhighlight_red%28+%28-highlight_red%28+10+%29%29%2Ax+%29-5=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+10+%29\"$
It becomes $\"x%5E2-highlight_green%28+10+%29%2Ax-5=0\"$ .
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Look at $\"highlight_red%28+x%5E2-10%2Ax-5+%29=0\"$ .
Equation $\"highlight_red%28+x%5E2-10%2Ax-5=0+%29\"$ is a quadratic equation: x^2-10*x-5 =0, and has solutions 10.4772255750517,-0.477225575051661
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=10.4772255750517,x=-0.477225575051661.

Universal Simplifier and Solver

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Done!

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