document.write( "Question 761739: how to simplify x+ 3 + 2/x / 1- 4/x^2 \n" ); document.write( "

Algebra.Com's Answer #463449 by khv_maths(12) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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Graphical form: $\"x%2B3%2B%282%2Fx%29%2F%28%281-4%29%2F%28x%5E2%29%29\"$ simplifies to $\"x%2F3%2B3\"$
Text form: x+3+(2/x)/((1-4)/(x^2)) simplifies to x/3+3
Cartoon (animation) form: $\"simplify_cartoon%28+x%2B3%2B%282%2Fx%29%2F%28%281-4%29%2F%28x%5E2%29%29+%29\"$
For tutors: simplify_cartoon( x+3+(2/x)/((1-4)/(x^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

.
Remove unneeded parentheses around factor $\"highlight_red%28+1%2Fx%5E2+%29\"$
It becomes $\"x%2B3%2B%282%2Fx%29%2F%28%281-4%29%2Fhighlight_green%28+x%5E2+%29%29\"$ .
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Look at $\"x%2B3%2Bhighlight_red%28+%28highlight_red%28+2%2Fx+%29%29%2F%28%281-4%29%2Fx%5E2%29+%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$ , $\"highlight_red%28+1%2Fx+%29\"$
It becomes $\"x%2B3%2Bhighlight_green%28+2+%29%2Fhighlight_green%28+x+%29%2F%28%281-4%29%2Fx%5E2%29\"$ .
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Look at $\"x%2B3%2Bhighlight_red%28+2%2Fx%2F%28highlight_red%28+%281-4%29%2Fx%5E2+%29%29+%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1%2F%281-4%29+%29\"$ , $\"highlight_red%28+x%5E2+%29\"$
It becomes $\"x%2B3%2B2%2Fx%2Fhighlight_green%28+%281-4%29+%29%2Ahighlight_green%28+x%5E2+%29\"$ .
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Look at $\"x%2B3%2B2%2Fx%2F%28highlight_red%28+1+%29-highlight_red%28+4+%29%29%2Ax%5E2\"$ .
Added fractions or integers together
It becomes $\"x%2B3%2B2%2Fx%2F%28highlight_green%28+-3+%29%29%2Ax%5E2\"$ .
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Look at $\"x%2B3%2B2%2Fhighlight_red%28+x+%29%2F%28-3%29%2Ahighlight_red%28+x%5E2+%29\"$ .
Reduce similar several occurrences of $\"highlight_red%28+1%2Fx+%29\"$ to $\"highlight_green%28+x%5E%28-1%2B2%29+%29\"$
It becomes $\"x%2B3%2B2%2Ahighlight_green%28+x%5E%28-1%2B2%29+%29%2F%28-3%29\"$ .
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Look at $\"x%2Bhighlight_red%28+3+%29%2B2%2Ax%5E%28-1%2B2%29%2F%28-3%29\"$ .
Moved $\"3\"$ to the right of expression
It becomes $\"x%2B2%2Ax%5E%28-1%2B2%29%2F%28-3%29%2Bhighlight_green%28+3+%29\"$ .
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Look at $\"x%2B2%2Ax%5E%28highlight_red%28+-1+%29%2B2%29%2F%28-3%29%2B3\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"x%2B2%2Ax%5E%28-highlight_green%28+1+%29%2B2%29%2F%28-3%29%2B3\"$ .
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Look at $\"x%2B2%2Ax%5E%28-1%2B2%29%2F%28highlight_red%28+-3+%29%29%2B3\"$ .
Removed extra sign in front of $\"-3\"$
It becomes $\"x%2B2%2Ax%5E%28-1%2B2%29%2F%28-highlight_green%28+3+%29%29%2B3\"$ .
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Look at $\"x%2Bhighlight_red%28+2%2Ax%5E%28-1%2B2%29%2F%28-highlight_red%28+3+%29%29+%29%2B3\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1%2F3+%29\"$
It becomes $\"x-2%2Ax%5E%28-1%2B2%29%2Fhighlight_green%28+3+%29%2B3\"$ .
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Look at $\"x-2%2Ax%5E%28-highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2F3%2B3\"$ .
Added fractions or integers together
It becomes $\"x-2%2Ax%5E%28highlight_green%28+1+%29%29%2F3%2B3\"$ .
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Look at $\"x-2%2Ax%5Ehighlight_red%28+%281%29+%29%2F3%2B3\"$ .
Removing power of one $\"highlight_red%28+%281%29+%29\"$
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Look at $\"highlight_red%28+x+%29-highlight_red%28+2%2Ax%2F3+%29%2B3\"$ .
Eliminated similar terms $\"highlight_red%28+x+%29\"$ , $\"highlight_red%28+-2%2Ax%2F3+%29\"$ replacing them with $\"highlight_green%28+%281-2%2A1%2F3%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%281-2%2A1%2F3%29%2Ax+%29%2B3\"$ .
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Look at $\"%281-highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%29%2Ax%2B3\"$ .
Multiplied numerator integers
It becomes $\"%281-highlight_green%28+2+%29%2F3%29%2Ax%2B3\"$ .
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Look at $\"%28highlight_red%28+1+%29-highlight_red%28+2%2F3+%29%29%2Ax%2B3\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+1%2F3+%29%29%2Ax%2B3\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+1%2F3+%29%29%2Ax+%29%2B3\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$ , $\"highlight_red%28+1%2F3+%29\"$
It becomes $\"highlight_green%28+1+%29%2Fhighlight_green%28+3+%29%2Ax%2B3\"$ .
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Look at $\"highlight_red%28+1+%29%2F3%2Ax%2B3\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"x%2F3%2B3\"$ .
Result: $\"x%2F3%2B3\"$
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Universal Simplifier and Solver

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Done!

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