document.write( "Question 308993: $\"+1%2Fx+%2B+%281%29%2F%281+%2B+x%29+=+%28-3%29%2F%28x%5E2+%2B+x%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #220923 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
GreAt job using the formula system, I am impressed. \r
\n" ); document.write( "\n" ); document.write( " $\"+1%2Fx+%2B+1%2F%281+%2B+x%29+=+-3%2F%28x%5E2+%2B+x%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "combine the two fractions on the left like regular fractions\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B1%29%2Fx%2F%28x%2B1%29+%2B+x%2Fx%2F%28x%2B1%29+=+-3%2Fx%2F%28x%2B1%29\"$
\n" ); document.write( " $\"%28x%2B1%2Bx%29%2Fx%2F%28x%2B1%29+=+-3%2Fx%2Fx%2B1\"$
\n" ); document.write( " $\"%282x%2B1%2B3%29%2Fx%2F%28x%2B1%29+=+0\"$
\n" ); document.write( " $\"%282x%2B4%29%2Fx%2F%28x%2B1%29+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "x=-2\r
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Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values

Your Result:

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Graphical form: Equation $\"1%2Fx%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29\"$ was fully solved.
Text form: 1/x+1/(1+x)=-3/(x^2+x) simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+1%2Fx%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29+%29\"$
For tutors: simplify_cartoon( 1/x+1/(1+x)=-3/(x^2+x) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"1%2Fhighlight_red%28+x+%29%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29\"$ .
Replaced x with -2
It becomes $\"1%2Fhighlight_green%28+-2+%29%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29\"$ .
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Look at $\"1%2F-2%2B1%2F%281%2Bhighlight_red%28+x+%29%29=-3%2F%28x%5E2%2Bx%29\"$ .
Replaced x with -2
It becomes $\"1%2F-2%2B1%2F%281%2Bhighlight_green%28+-2+%29%29=-3%2F%28x%5E2%2Bx%29\"$ .
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Look at $\"1%2F-2%2B1%2F%28highlight_red%28+1+%29%2Bhighlight_red%28+-2+%29%29=-3%2F%28x%5E2%2Bx%29\"$ .
Added fractions or integers together
It becomes $\"1%2F-2%2B1%2F%28highlight_green%28+-1+%29%29=-3%2F%28x%5E2%2Bx%29\"$ .
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Look at $\"highlight_red%28+1%2F-2+%29%2Bhighlight_red%28+1%2F%28-1%29+%29=-3%2F%28x%5E2%2Bx%29\"$ .
Replace constants in expression: $\"highlight_red%28+1%2F-2+%29\"$ , $\"highlight_red%28+1%2F%28-1%29+%29\"$ with $\"highlight_green%28+-1.5+%29\"$
It becomes $\"highlight_green%28+-1.5+%29=-3%2F%28x%5E2%2Bx%29\"$ .
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Look at $\"highlight_red%28+-1.5+%29=-3%2F%28x%5E2%2Bx%29\"$ .
Removed extra sign in front of $\"-1.5\"$
It becomes $\"-highlight_green%28+1.5+%29=-3%2F%28x%5E2%2Bx%29\"$ .
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Look at $\"-1.5=-3%2F%28highlight_red%28+x+%29%5E2%2Bx%29\"$ .
Replaced x with -2
It becomes $\"-1.5=-3%2F%28highlight_green%28+-2+%29%5E2%2Bx%29\"$ .
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Look at $\"-1.5=-3%2F%28highlight_red%28+-2+%29%5Ehighlight_red%28+2+%29%2Bx%29\"$ .
Replace constants in factor: $\"highlight_red%28+-2+%29\"$ , $\"highlight_red%28+2+%29\"$ with $\"highlight_green%28+4+%29\"$
It becomes $\"-1.5=-3%2F%28highlight_green%28+4+%29%2Bx%29\"$ .
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Look at $\"-1.5=-3%2F%284%2Bhighlight_red%28+x+%29%29\"$ .
Replaced x with -2
It becomes $\"-1.5=-3%2F%284%2Bhighlight_green%28+-2+%29%29\"$ .
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Look at $\"-1.5=-3%2F%28highlight_red%28+4+%29%2Bhighlight_red%28+-2+%29%29\"$ .
Added fractions or integers together
It becomes $\"-1.5=-3%2F%28highlight_green%28+2+%29%29\"$ .
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Look at $\"-1.5=-highlight_red%28+3%2F%28highlight_red%28+2+%29%29+%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1%2F2+%29\"$
It becomes $\"-1.5=-3%2Fhighlight_green%28+2+%29\"$ .
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Look at $\"-1.5=highlight_red%28+-3%2F2+%29\"$ .
Moved these terms to the left $\"highlight_green%28+3%2F2+%29\"$
It becomes $\"-1.5%2Bhighlight_green%28+3%2F2+%29=0\"$ .
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Look at $\"-highlight_red%28+1.5+%29%2Bhighlight_red%28+3%2F2+%29=0\"$ .
Added fractions or integers together
It becomes $\"highlight_green%28+0%2F10+%29=0\"$ .
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Look at $\"highlight_red%28+0+%29%2Fhighlight_red%28+10+%29=0\"$ .
Factors 0 and 10 have greatest common factor (GCF) of 10. Reducing fraction.
It becomes $\"highlight_green%28+0+%29%2Fhighlight_green%28+1+%29=0\"$ .
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Look at $\"highlight_red%28+0%2F1+%29=0\"$ .
Since $\"highlight_red%28+0%2F1+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"0=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1%2F1+%29\"$
It becomes $\"0=0\"$ .
Result: $\"0=0\"$
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Universal Simplifier and Solver

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Done!

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