document.write( "Question 68598This question is from textbook An Incremental Development
\n" ); document.write( ": PLease help to simplify by adding like terms :\r
\n" ); document.write( "\n" ); document.write( "{a/x - 3a^2*c^0x^-1 / a) + (4x^-1 / aa^-2) \n" ); document.write( "

Algebra.Com's Answer #48815 by ichudov(507) $\"\"$ $\"About$

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: $\"%28a%2Fx-3a%5E2%2Ac%5E0x%5E-1%2Fa%29%2B%284x%5E-1%2Fa%2Aa%5E-2%29\"$ simplifies to $\"-2%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$
Text form: (a/x-3a^2*c^0x^-1/a)+(4x^-1/a*a^-2) simplifies to -2*a/x+4/x/a^3
Cartoon (animation) form: $\"simplify_cartoon%28+%28a%2Fx-3a%5E2%2Ac%5E0x%5E-1%2Fa%29%2B%284x%5E-1%2Fa%2Aa%5E-2%29+%29\"$
For tutors: simplify_cartoon( (a/x-3a^2*c^0x^-1/a)+(4x^-1/a*a^-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

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Remove unneeded parentheses around terms $\"highlight_red%28+a%2Fx+%29\"$ , $\"highlight_red%28+-3%2Aa%5E2%2Ac%5E0%2Ax%5E-1%2Fa+%29\"$
It becomes

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Look at $\"a%2Fx-3%2Aa%5E2%2Ac%5E0%2Ax%5E-1%2Fa%2Bhighlight_red%28+%284%2Ax%5E-1%2Fa%2Aa%5E-2%29+%29\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+4%2Ax%5E-1%2Fa%2Aa%5E-2+%29\"$
It becomes $\"a%2Fx-3%2Aa%5E2%2Ac%5E0%2Ax%5E-1%2Fa%2Bhighlight_green%28+4%2Ax%5E-1%2Fa%2Aa%5E-2+%29\"$ .
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Look at

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Removing power $\"highlight_red%28+c+%29\"$ to degree of $\"highlight_green%28+0+%29\"$
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Look at

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Reduce similar several occurrences of $\"highlight_red%28+a%5E2+%29\"$ to $\"highlight_green%28+a%5E%28-1%2B2%29+%29\"$
It becomes $\"a%2Fx-3%2Ahighlight_green%28+a%5E%28-1%2B2%29+%29%2A1%2Ax%5E-1%2B4%2Ax%5E-1%2Fa%2Aa%5E-2\"$ .
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Look at

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Reduce similar several occurrences of $\"highlight_red%28+1%2Fa+%29\"$ to $\"highlight_green%28+a%5E%28-1%2B-2%29+%29\"$
It becomes

.
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Look at

.
Removed extra sign in front of $\"-1\"$
It becomes

.
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Look at

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Removed extra sign in front of $\"-1\"$
It becomes

.
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Look at

.
Removed extra sign in front of $\"-2\"$
It becomes $\"a%2Fx-3%2Aa%5E%28-1%2B2%29%2A1%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28-1-highlight_green%28+2+%29%29\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"a%2Fx-highlight_green%28+3+%29%2Aa%5E%28-1%2B2%29%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28-1-2%29\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"a%2Fx-3%2Aa%5E%28-1%2B2%29%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28highlight_green%28+-3+%29%29\"$ .
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Look at $\"a%2Fx-3%2Aa%5E%28-1%2B2%29%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28highlight_red%28+-3+%29%29\"$ .
Removed extra sign in front of $\"-3\"$
It becomes $\"a%2Fx-3%2Aa%5E%28-1%2B2%29%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28-highlight_green%28+3+%29%29\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"a%2Fx-3%2Aa%5E%28highlight_green%28+1+%29%29%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28-3%29\"$ .
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Look at $\"a%2Fx-3%2Aa%5Ehighlight_red%28+%281%29+%29%2Ax%5E-1%2B4%2Ax%5E-1%2Aa%5E%28-3%29\"$ .
Removing power of one $\"highlight_red%28+%281%29+%29\"$
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Look at $\"a%2Fx-3%2Aa%2Ahighlight_red%28+x%5E-1+%29%2B4%2Ax%5E-1%2Aa%5E%28-3%29\"$ .
Negative power changes multiplication to division
It becomes $\"a%2Fx-3%2Aa%2Fhighlight_green%28+x%5E1+%29%2B4%2Ax%5E-1%2Aa%5E%28-3%29\"$ .
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Look at $\"a%2Fx-3%2Aa%2Fx%5E1%2B4%2Ahighlight_red%28+x%5E-1+%29%2Aa%5E%28-3%29\"$ .
Negative power changes multiplication to division
It becomes $\"a%2Fx-3%2Aa%2Fx%5E1%2B4%2Fhighlight_green%28+x%5E1+%29%2Aa%5E%28-3%29\"$ .
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Look at $\"a%2Fx-3%2Aa%2Fx%5E1%2B4%2Fx%5E1%2Ahighlight_red%28+a%5E%28-3%29+%29\"$ .
Negative power changes multiplication to division
It becomes $\"a%2Fx-3%2Aa%2Fx%5E1%2B4%2Fx%5E1%2Fhighlight_green%28+a%5E3+%29\"$ .
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Look at $\"a%2Fx-3%2Aa%2Fx%5Ehighlight_red%28+1+%29%2B4%2Fx%5E1%2Fa%5E3\"$ .
Removing power of one $\"highlight_red%28+1+%29\"$
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Look at $\"a%2Fx-3%2Aa%2Fx%2B4%2Fx%5Ehighlight_red%28+1+%29%2Fa%5E3\"$ .
Removing power of one $\"highlight_red%28+1+%29\"$
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Look at $\"highlight_red%28+a%2Fx+%29-highlight_red%28+3%2Aa%2Fx+%29%2B4%2Fx%2Fa%5E3\"$ .
Eliminated similar terms $\"highlight_red%28+a%2Fx+%29\"$ , $\"highlight_red%28+-3%2Aa%2Fx+%29\"$ replacing them with $\"highlight_green%28+%281-3%29%2Aa%2Fx+%29\"$
It becomes $\"highlight_green%28+%281-3%29%2Aa%2Fx+%29%2B4%2Fx%2Fa%5E3\"$ .
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Look at $\"%28highlight_red%28+1+%29-highlight_red%28+3+%29%29%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-2+%29%29%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$ .
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Look at $\"%28highlight_red%28+-2+%29%29%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$ .
Removed extra sign in front of $\"-2\"$
It becomes $\"%28-highlight_green%28+2+%29%29%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+2+%29%29%2Aa%2Fx+%29%2B4%2Fx%2Fa%5E3\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"-highlight_green%28+2+%29%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$ .
Result: $\"-2%2Aa%2Fx%2B4%2Fx%2Fa%5E3\"$
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Universal Simplifier and Solver

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Done!

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