Question

Answer 1

a: \(\frac{x^2-y^2}{\left(x+y\right)\left(ay-ax\right)}\)

\(=\frac{\left(x-y\right)\left(x+y\right)}{\left(x+y\right)\cdot\left(-a\right)\cdot\left(x-y\right)}=\frac{1}{-a}=\frac{-1}{a}\)

b: \(\frac{2ax-2x-3y+3ay}{4ax+6x+9y+6ay}-\frac{ax^2-a}{\left(x+1\right)\left(x-1\right)}\)

\(=\frac{2x\left(a-1\right)+3y\left(a-1\right)}{2x\left(2a+3\right)+3y\left(2a+3\right)}-\frac{a\left(x^2-1\right)}{x^2-1}=\frac{a-1}{2a+3}-a\)

\(=\frac{\left(a-1-2a^2-3a\right)}{2a+3}=\frac{-2a^2-2a-1}{2a+3}\)