Question

How do you simplify and find the excluded values of `(x-2)/(x^2+3x-10)`?

Answer 1

`1/(x+5)`, but `x != -5 and x !=2`

Explanation:

The denominator of the fraction can be factorised.

`(x - 2)/((x+5)(x-2))`

The denominator may not be zero, so we need to find which values of x would give 0 for each factor.

If `x + 5 = 0 rArr x = -5` and if `x-2 = 0 rArr x = 2`

The fraction simplifies to

`cancel(x - 2)/((x+5)cancel(x-2)) = 1/(x+5)`