SOLUTION: PLease help to simplify by adding like terms : {a/x - 3a^2*c^0x^-1 / a) + (4x^-1 / aa^-2)

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

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • 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.

DETAILED EXPLANATION

Look at .
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 .
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.
Look at .
Removing power highlight_red%28+c+%29 to degree of highlight_green%28+0+%29
Look at .
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.
Look at .
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 .
Look at .
Removed extra sign in front of -1
It becomes .
Look at .
Removed extra sign in front of -1
It becomes .
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.
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.
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.
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.
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.
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
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.
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.
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.
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
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
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.
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.
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.
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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Done!