Question

How do you find the zeros of `f(x)=(x^2-3x-4)/(x^2-x-12)`?

Answer 1

`x=-1`

Explanation:

Factorising and simplifying f(x) as follows.

`f(x)=(x^2-3x-4)/(x^2-x-12)=(cancel((x-4))(x+1))/(cancel((x-4))(x-3))=(x+1)/(x-3)`

with exclusion x ≠ 4

The zeros of f(x) are the values of x which make f(x) equal zero. That is f(x)=0.

For `f(x)=(x+1)/(x+3)`

The denominator of f(x) cannot be zero as this would make f(x) undefined. The numerator is the only part of the rational function that can equal zero.

`rArrx+1=0rArrx=-1" is the zero of f(x)"`