At which values of x does the function f(x) have a vertical asymptote? check all that apply

The values of x are -6 , 0 , 1 ⇒ Answers C , D , E

Step-by-step explanation:

* Let revise how to find the vertical asymptote

- Vertical asymptotes of a rational function f(x)/g(x) can be found by

 solving the equation g(x) = 0 ⇒ the denominator of the fraction

- Note: this only applies if the numerator f(x) is not zero for the same

 x value

* Lets solve the problem

∵ F(x) = 1/x(x + 6)(x - 1)

∵ The denominator of the fraction is x(x + 6)(x - 1)

- To find the equation of the vertical asymptote Put the

 denominator = 0

∴ x(x + 6)(x - 1) = 0

- The denominator has three factors, equate each by 0

∴ x = 0

OR

∴ x + 6 = 0 ⇒ subtract 6 from both sides

∴ x = -6

OR

x - 1 = 0 ⇒ add 1 to both sides

∴ x = 1

∴ From all above there are 3 vertical asymptotes at x = -6 , 0 , 1

* The answers are C, D , E

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b