Question

\(\left(\dfrac{1-x^2-11}{x+1}\right).\left(\dfrac{3+x}{x-3}-\dfrac{36}{9-x^2}-\dfrac{x-3}{x+3}\right)\)

Answer 1

\(\left(\dfrac{1-x^2-11}{x+1}\right)\cdot\left(\dfrac{3+x}{x-3}-\dfrac{36}{9-x^2}-\dfrac{x-3}{x+3}\right)\)

\(=\dfrac{-x^2-10}{x+1}\cdot\dfrac{\left(x+3\right)^2+36-\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{-x^2-10}{x+1}\cdot\dfrac{x^2+6x+9+36-x^2+6x-9}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{-x^2-10}{x+1}\cdot\dfrac{12x+36}{\left(x-3\right)\left(x+3\right)}=\dfrac{12\left(-x^2-10\right)}{\left(x-3\right)\left(x+1\right)}\)