Question

question
find all vertical asymptotes of the following function.
f(x) = \frac{2x - 2}{5x^{2}-36x - 32}

Explanation:

Step1: Set the denominator equal to 0

$5x^{2}-36x - 32=0$

Step2: Factor the quadratic equation

We need to find two numbers that multiply to $5\times(- 32)=-160$ and add up to -36. The numbers are -40 and 4.
$5x^{2}-40x + 4x-32 = 0$
$5x(x - 8)+4(x - 8)=0$
$(5x + 4)(x - 8)=0$

Step3: Solve for x

Set each factor equal to 0:
For $5x+4 = 0$, we get $x=-\frac{4}{5}$;
For $x - 8=0$, we get $x = 8$.

Answer:

$x=-\frac{4}{5},x = 8$