Question

How do you simplify `(x^2-3x+2)/(x^2+5x-6)`?

Answer 1

`(x-2)/(x+6)`

Explanation:

The first step is to factorise both numerator and denominator.

Both are quadratics and can be factorised using the a-c method.

`rArrx^2-3x+2=(x-2)(x-1)`

and `x^2+5x-6=(x+6)(x-1)`

`rArr(x^2-3x+2)/(x^2+5x-6)=((x-2)(cancel(x-1)))/((x+6)(cancel(x-1)))=(x-2)/(x+6)`