Question

Please help with this vertical asymptote of rational functions problem

Answer 1

The expression can be written in simplified form as:

$f(x)= \frac{5x+10}{ x^{2} +7x+10} \\ \\ f(x)= \frac{5(x+2)}{ x^{2} +2x+5x+10} \\ \\ f(x)= \frac{5(x+2)}{(x+2)(x+5)}$

x+2 occurs in both numerator and denominator. This means there is a hole at x=-2, this can also be seen from the graph.

So, the vertical asymtptote will occur at the point where:
x+5=0
⇒
x = -5

So, option A gives the correct equation of the vertical asymptote of the function

Answer 2

The answer is the first option, which is:

 x=-5

 The explanation is shown below:

1.To solve this problem you must apply the proccedure shown below:

 2. You must factor the denominator, as following:

 f(x)=(5x+10)/(x^2+7x+10)
 f((x)=(5x+10)/(x+2)(x+5)

 x+5=0
 x=-5