question find all vertical asymptotes of the following function. f(x) = (25x² - 64)/(15x + 24) answer no…

question find all vertical asymptotes of the following function. f(x) = (25x² - 64)/(15x + 24) answer no vertical asymptotes submit answer

question find all vertical asymptotes of the following function. f(x) = (25x² - 64)/(15x + 24) answer no vertical asymptotes submit answer

Answer

Answer:

$x = -\frac{8}{5}$

Explanation:

Step1: Set denominator equal to 0

$15x + 24=0$

Step2: Solve for x

$15x=-24$ $x = -\frac{24}{15}=-\frac{8}{5}$

Step3: Check for common factors

Factor numerator $25x^{2}-64=(5x + 8)(5x - 8)$. The factor $5x + 8$ is not a factor of the denominator $15x + 24 = 3(5x+8)$ in a way that would cancel out the zero - point. So $x = -\frac{8}{5}$ is a vertical asymptote.