question 30 (1 point) f(x)=(x² - 1)(x² + 3x + 2)/(x² - 1)²(x + 2)(x - 3) find the values of x where the…

question 30 (1 point) f(x)=(x² - 1)(x² + 3x + 2)/(x² - 1)²(x + 2)(x - 3) find the values of x where the function has a removable discontinuity. a 1,-1,-2 b -2,1 c -1,-2 d 3,-1,1,-2 e none of these

question 30 (1 point) f(x)=(x² - 1)(x² + 3x + 2)/(x² - 1)²(x + 2)(x - 3) find the values of x where the function has a removable discontinuity. a 1,-1,-2 b -2,1 c -1,-2 d 3,-1,1,-2 e none of these

Answer

Explanation:

Step1: Factor the expressions

Factor $x^{2}-1=(x - 1)(x + 1)$, $x^{2}+3x + 2=(x + 1)(x+2)$. Then $f(x)=\frac{(x - 1)(x + 1)(x + 1)(x + 2)}{(x - 1)^{2}(x + 1)^{2}(x + 2)(x - 3)}$.

Step2: Identify removable discontinuities

A removable discontinuity occurs when a factor in the numerator and denominator cancels out. The factors that can be canceled are $(x + 1)$ and $(x + 2)$. Setting $x+1 = 0$ gives $x=-1$ and setting $x + 2=0$ gives $x=-2$.

Answer:

C. -1, -2