Find the vertical asymptotes if any of the graph of the rati

Find the vertical asymptotes, if any, of the graph of the rational function. h(x) = x + 1/x^2 - 1 f(x) = x/x^2 + 4

Solution

Solution:

Given h(x) = x+1/(x²-1)

We mus set the denominator equal to 0

x²-1 = 0

(x²-1²) = 0

(x-1) (x+1) = 0

Therefore x = 1, - 1

There are vertical asymptotes at x = -1, x = 1

2)

Given f(x) = x/(x²+4)

We mus set the denominator equal to 0

x²+4 = 0

x²+2² = 0

(x+2) (x-2) = 0

x = -2,2

There are vertical asymptotes at x = -2, x = 2