SOLUTION: {{{ (1)/(a-b) - (a*b)/(a^3-b^3) }}} i know the answer is {{{ (a^2+b^2)/(a^3-b^3) }}} but how do i get to the answer?

Algebra ->  Equations -> SOLUTION: {{{ (1)/(a-b) - (a*b)/(a^3-b^3) }}} i know the answer is {{{ (a^2+b^2)/(a^3-b^3) }}} but how do i get to the answer?      Log On


   

Question 1057007: +%281%29%2F%28a-b%29+-+%28a%2Ab%29%2F%28a%5E3-b%5E3%29+ i know the answer is +%28a%5E2%2Bb%5E2%29%2F%28a%5E3-b%5E3%29+ but how do i get to the answer?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Factorize the Difference Of Cubes denominator, and apply the simplest common denominator.


Fraction skills which you already know. Nothing is different except you have expressions instead of plain base ten type numbers.

You know the difference of squares. You should know or be able to figure out the difference of cubes. If not, look up this in your book. Your book should show you a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29.

YOU DO IT!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

+%281%29%2F%28a-b%29+-+%28a%2Ab%29%2F%28a%5E3-b%5E3%29+ i know the answer is +%28a%5E2%2Bb%5E2%29%2F%28a%5E3-b%5E3%29+ but how do i get to the answer?
1%2F%28a+-+b%29+-+ab%2F%28a%5E3+-+b%5E3%29

1%2F%28a+-+b%29+-+ab%2F%28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29 ------ Factoring DENOMINATOR of 2nd fraction: a%5E3+-+b%5E3

%28a%5E2+%2B+ab+%2B+b%5E2+-+ab%29%2F%28%28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29%29 ----------- Multiplying each fraction by LCD, %28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29