Respuesta :
Answer:
x cannot equal -3, and x cannot equal -2
Step-by-step explanation:
Answer:
The excluded values of the rational expression are -3 and -2.
Step-by-step explanation:
If a ration function is defined as [tex]R(x)=\frac{p(x)}{q(x)}[/tex], then the excluded values of the rational function are those values for which q(x)=0.
The given rational expression is
[tex]\frac{x^2+2x-3}{x^2+5x+6}[/tex]
Factories the numerator and denominator.
[tex]\frac{x^2+3x-x-3}{x^2+3x+2x+6}[/tex]
[tex]\frac{x(x+3)-1(x+3)}{x(x+3)+2(x+3)}[/tex]
[tex]\frac{(x+3)(x-1)}{(x+3)(x+2)}[/tex] .... (1)
Equate the denominator equal to 0.
[tex](x+3)(x+2)=0[/tex]
Using zero product property,
[tex]x+3=0\Rightarrow x=-3[/tex]
[tex]x+2=0\Rightarrow x=-2[/tex]
Therefore the excluded values of the rational expression are -3 and -2.
Cancel out the common factors of equation (1)
[tex]\frac{x - 1}{x + 2}[/tex] for (x≠-3)
It means x=-2 is vertical asymptote and x=-3 is hole.
