Asymptotes/denominator questions

Question

Equation: y=(3/x+5)-(16/x)-1

1.) Name any vertical asymptote(s) and explain why they are asymptotes.

2.) Name the least common denominator. Explain how using the LCD helps us solve this problem.

Answer 1

Vertical asymptotes appear when there would be a 1/0 in the equation.

This happens when x = -5 and 0

(3/-5+5) = 3/0 asymptote

The least common denominator will be just x(x + 5)

This is just the denominators multiplied together which is always the maximum for the least common denominator.

If you set this equal to zero you will find that when x = 0 and -5 it will.