Question

Simplify the following expression:
$(m+n-\frac{4mn}{m+n}):(\frac{m}{m+n}-\frac{n}{n-m}-\frac{2mn}{m^2-n^2})$

Answer 1

$(\frac{(m+n{)}^2-4mn}{m+n}):(\frac{m}{m+n}+\frac{n}{m-n}-\frac{2mn}{m^2-n^2})=(\frac{(m-n{)}^2}{m+n}):(\frac{m^2-mn+mn+n^2-2mn}{m^2-n^2})=(\frac{(m-n{)}^2}{m+n}):(\frac{(m-n{)}^2}{m^2-n^2})=m-n:1$