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

Question

asked Dec 21, 2020 18.1k views

2 Answers

NinMonkey · Answer 1 · 2020-12-25T18:10:23+0000

Answer:

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.