Problem

Find the vertical asymptotes, if any, of the graph of the rational function. \[ h(x)=\frac{x+2}{x^{2}-4} \] (A) no vertical asymptote (B) $x=2, x=-2$ $x=2$ $x=-2$

Solution

Step 1 :Find the values of x for which the denominator is equal to zero: \(x^2 - 4 = (x - 2)(x + 2)\)

Step 2 :The denominator is zero when \(x = 2\) or \(x = -2\)

Step 3 :Check if the numerator is also zero at these points: \(x + 2\)

Step 4 :The numerator is zero when \(x = -2\)

Step 5 :Since the numerator and denominator are both zero at \(x = -2\), it is not a vertical asymptote

Step 6 :\(\boxed{x=2, x=-2}\) are the vertical asymptotes

From Solvely APP
Source: https://solvelyapp.com/problems/16081/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download