Question

What is the simplified form of the rational expression below 6x^2-54 / 5x^2+15x

Answer 1

`\large\boxed{(6x^2-54)/(5x^2+15x)=(6(x-3))/(5x)=(6x-18)/(5x)}`

Explanation:

`6x^2-54\qquad\text{distributive}\\\\=6(x^2-9)=6(x^2-3^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=6(x-3)(x+3)\\\\5x^2+15x\qquad\text{distributive}\\\\=5x(x+3)\\-----------------\\\\(6x^2-54)/(5x^2+15x)=(6(x-3)(x+3))/(5x(x+3))\qquad\text{cancel}\ (x+3)\\\\=(6(x-3))/(5x)=(6x-18)/(5x)`