Question

Answer 1

\(\left(\dfrac{y^2}{y^2-36}-\dfrac{y-6}{y+6}\right)\dfrac{y^2-36}{y-3}\left(y\ne\pm6;y\ne3\right).\)

\(=\dfrac{y^2-\left(y-6\right)^2}{\left(y-6\right)\left(y+6\right)}.\dfrac{\left(y-6\right)\left(y+6\right)}{y-3}.\)

\(=\dfrac{\left(y-y+6\right)\left(y+y-6\right)}{y-3}=\dfrac{6\left(2y-6\right)}{y-3}.\)

\(=\dfrac{12\left(y-3\right)}{y-3}=12.\)

Answer 2

\(=\dfrac{y^2-y^2+12y-36}{\left(y-6\right)\left(y+6\right)}\cdot\dfrac{\left(y-6\right)\left(y+6\right)}{y-3}=\dfrac{12\left(y-3\right)}{y-3}=12\)