Question

How do you simplify `(x^2 - x - 6) /( x^2 - 4)`?

Answer 1

`= (x-3)/(x-2)`

Explanation:

We may not cancel in the numerator or denominator because there is not only one term. The + and - signs show there are 3 terms in the numerator an two terms in the denominator.

However, if we factorise we will only have one term and then we may cancel.
The numerator is a quadratic trinomial and the denominator is the difference between two squares.

`(x^2 - x - 6)/(x^2 - 4) = ((x-3)(x+2))/((x+2)(x-2))`

`((x-3)cancel((x+2)))/(cancel((x+2))(x-2))`

`= (x-3)/(x-2)`