Find the vertical asymptotes of the rational function.
-$$f ( x ) = \frac { - 2 x ( x + 2 ) } { 3 x ^ { 2 } - 5 x - 8 }$$
A) $x = \frac { 8 } { 3 } , x = - 1$
B) $x = - \frac { 8 } { 3 } , x = 1$
C) $x = - \frac { 3 } { 8 } , x = 1$
D) $x = \frac { 3 } { 8 } , x = - 1$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (and the numerator is not zero at those points). For the given function, set the denominator equal to zero and solve for $x$: $3x^2 - 5x - 8 = 0$. Factoring or using the quadratic formula, we find the roots $x = \frac{8}{3}$ and $x = -1$, which are the points where the function has vertical asymptotes.

Find the Vertical Asymptotes of the Rational Function f(x)=−2x(x+2)3x2−5x−8f ( x ) = \frac { - 2 x ( x + 2 ) } { 3 x ^ { 2 } - 5 x - 8 }f(x)=3x2−5x−8−2x(x+2)​

Find the Vertical Asymptotes of the Rational Function $f ( x ) = \frac { - 2 x ( x + 2 ) } { 3 x ^ { 2 } - 5 x - 8 }$