Question

Divide and state the quotient in simplest form. x^2-9⁢x+18/x+1 ÷x^2+x-12/x+1

Answer 1

$\dfrac{x^2-9x+18}{x+1}\div\dfrac{x^2+x-12}{x+1}=\dfrac{x^2-9x+18}{x+1}\cdot\dfrac{x+1}{x^2+x-12}\\\\=\dfrac{x^2-9x+18}{x^2+x-12}=\dfrac{x^2-6x-3x+18}{x^2+4x-3x-12}=\dfrac{x(x-6)-3(x-6)}{x(x+4)-3(x+4)}\\\\=\dfrac{(x-6)(x-3)}{(x+4)(x-3)}=\dfrac{x-6}{x+4}$