Question

Identify the excluded values of the rational expression x^2+2x-3/x^2+5x+6

Answer 1

x cannot equal -3, and x cannot equal -2

Explanation:

Answer 2

The excluded values of the rational expression are -3 and -2.

Explanation:

If a ration function is defined as
`R(x)=(p(x))/(q(x))`, then the excluded values of the rational function are those values for which q(x)=0.

The given rational expression is

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

Factories the numerator and denominator.

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

`(x(x+3)-1(x+3))/(x(x+3)+2(x+3))`

`((x+3)(x-1))/((x+3)(x+2))` .... (1)

Equate the denominator equal to 0.

`(x+3)(x+2)=0`

Using zero product property,

`x+3=0\Rightarrow x=-3`

`x+2=0\Rightarrow x=-2`

Therefore the excluded values of the rational expression are -3 and -2.

Cancel out the common factors of equation (1)

`(x - 1)/(x + 2)` for (x≠-3)

It means x=-2 is vertical asymptote and x=-3 is hole.