Question

I need help on this ASAP. Please simplify the problem below.

Answer 1

1

Explanation:

You want to simplify the given complex fraction involving fractional powers.

Simplify

We can define a = x^(1/2) and b = y^(1/2) to remove fractional powers from the expression. The rest of it involves factoring the sum of cubes and the difference of squares. Common factors are cancelled.

`\left((a^3+b^3)/(a^2-b^2)-(a^2)/(a+b)-(b^2)/(a-b)\right)/(ab)/(a+b)\\\\=\left((a^3+b^3)/(a^2-b^2)-(a^2)/(a+b)-(b^2)/(a-b)\right)*(a+b)/(ab)\\\\=\left(((a^3+b^3)-a^2(a-b)-b^2(a+b))/(a^2-b^2)\right)*(a+b)/(ab)\\\\=((a^3+b^3-a^3+a^2b-ab^2-b^3)(a+b))/(ab(a-b)(a+b))=(a^2b-ab^2)/(ab(a-b))=(a^2b-ab^2)/(a^2b-ab^2)\\\\=\boxed{1}`

Note that there are no instances of 'a' or 'b' left in the expression, so we do not need to back-substitute for 'a' and/or 'b' in the simplified form.