Question

How do you simplify `(x^2 - 7x + 6)/(x^2-36)`?

Answer 1

`(x^2-7x+6)/(x^2-36)=color(green)((x-1)/(x+6)`
(assuming `x!=+-6` so the original expression is valid).

Explanation:

Factoring
`color(white)("XXX")x^2-7x+6 = (x-6)(x-1)`

`color(white)("XXX")x^2-36=(x-6)(x+6)`

So
`color(white)("XXX")(x^2-7x+6)/(x^2-36)=(cancel(""(x-6))(x-1))/(cancel(""(x-6))(x+6)`