Question

Find the values of x for which the denominator is equal to zero for y=3x+6/x^2-5x+6

Answer 1

x = 2

and

x = 3

Explanation:

The function given is:

`y=(3x+6)/(x^2-5x+6)`

In this fraction, the bottom part is the denominator. We need to set it equal to 0 and solve for 2 values of x.

`x^2-5x+6=0\\x^2-3x-2x+6=0\\x(x-3)-2(x-3)=0\\(x-2)(x-3)=0\\x=2,3`

This is middle term factorization process. Hence the 2 solutions (roots) of the denominator is:

x = 2, 3