How to factor a fraction with exponents?

Question

I am given this problem and would appreciate any help in finishing where I get stuck.

a^3-ab^2 16 16(a^3-ab^2) 4(a^3-ab^2)

------------ x ---------------- = ---------------------= ------------------- From this point I am unsure how to finish

12 ab^2+b^3 12(ab^2+b^3) 3(ab^2+b^3) the factoring.

Thanks,

Brian

Answer 1

You can factor "a" from the numerator and b² from the denominator.

... = 4a(a² - b²) / [3b²(a + b)]

Note that

a² - b² = (a - b)(a + b)

So now you have

... = 4a(a - b)(a + b) / [3b²(a + b)] = 4a(a - b) / (3b²)

This is as far as you can simplify.