Question

Create a rational expression that satisfies the following criteria: 1) Domain is all reals except 1 and -1 2) x=1 is a vertical asymptote 3) X = -1 is a hole 4) There is a horizontal asymptote at y = 3

Answer 1

y = (3x² + x - 2)/(x² - 1)

Explanation:

(x - 1)(x + 1) = x² - 1

In the denominator

f(x)/(x² - 1)

f(x) has a factor (x + 1)

3 + (x + 1)/(x² - 1)

(3x² - 3 + x + 1)/(x² - 1)

y = (3x² + x - 2)/(x² - 1)