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

1 Answer
Jun 24, 2016

Answer:

#= (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)#