Question

Divide and state the quotient in simplest form.

x^2-9⁢x+18/x+1 ÷x^2+x-12/x+1

Answer 1

`(x^2-9x+18)/(x+1)/(x^2+x-12)/(x+1)=(x^2-9x+18)/(x+1)\cdot(x+1)/(x^2+x-12)\\\\=(x^2-9x+18)/(x^2+x-12)=(x^2-6x-3x+18)/(x^2+4x-3x-12)=(x(x-6)-3(x-6))/(x(x+4)-3(x+4))\\\\=((x-6)(x-3))/((x+4)(x-3))=(x-6)/(x+4)`