SOLUTION: what are the steps to solving a^2-b^2/a^3-b^3

Question 542491: what are the steps to solving a^2-b^2/a^3-b^3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you start with:
(a^2 - b^2) / (a^3 - b^3)
you factor the numerator to get:
[(a-b)*(a+b)] / (a^3 - b^3)
you factor the denominator to get:
[(a-b)*(a+b)] / [(a-b)*(a^2+ab+b^2)]
the (a-b) in the numerator and the denominator cancel out and you are left with:
(a+b) / (a^2+ab+b^2)
since you can't factor (a^2+ab+b^2) any further, that's your answer.
you needed to know the special formulas involved.
those are:
(a^2 - b^2) = (a-b)(a+b)
(a^3-b^3) = (a-b)(a^2+ab+b^2)
they should be in your text.
they are also in the following lesson on factoring polynomials from wtamu.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm
look for the section on "factoring a sum of two cubes" and "factoring a difference of two cubes".
the whole tutorial is worth a read.

RELATED QUESTIONS
What are the steps to solving the equation 3/8x + 15/2? Choose a,b,c or d and explain why (answered by solver91311)

what are the steps to solving a=bc/b+c for... (answered by ankor@dixie-net.com,dabanfield,rapaljer)

solve for b: =5(2-b)-4(1-3b) (a)- 3/2 (b)6/7 (c)3/2 (d)3/10 (e)none of these what... (answered by jim_thompson5910)

What are the steps to the problem ∛(a^2 b^2 )∙√(a^2 b^3 )? I already... (answered by lwsshak3)

What are the steps to solving this equation? x^-3 + y ^-6 -------------- x^-6... (answered by checkley77)

2[8-4(3-x)]-2=8[2(4x-3)+7]-50 what are the steps to solving the problem? (answered by Alan3354,MathLover1)

Solving for B...... (answered by sheldonbbtrocks)

What are the steps to factor the expression x^2-(a+b)x+ab down to... (answered by josgarithmetic)

a=b+3(4-c) b=5 c=2 what is a ,i need to know how the process is done to get the value... (answered by jim_thompson5910)