Question

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

Answer 1

Answer:

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

Step-by-step explanation:

If a ration function is defined as $R(x)=\frac{p(x)}{q(x)}$, then the excluded values of the rational function are those values for which q(x)=0.

The given rational expression is

$\frac{x^2+2x-3}{x^2+5x+6}$

Factories the numerator and denominator.

$\frac{x^2+3x-x-3}{x^2+3x+2x+6}$

$\frac{x(x+3)-1(x+3)}{x(x+3)+2(x+3)}$

$\frac{(x+3)(x-1)}{(x+3)(x+2)}$                .... (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)

$\frac{x - 1}{x + 2}$ for (x≠-3)

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

Answer 2

Answer:

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

Step-by-step explanation: