# What are the asymptotes for ((x+2)(x+5))/(x+2)?

Aug 7, 2015

There are no vertical or horizontal asymptotes

#### Explanation:

$y = \frac{\left(x + 2\right) \left(x + 5\right)}{x + 2}$

Step 1. Cross out any factors in both the numerator and denominator.

y=color(red)(cancel(color(black)("("x+2")"))color(black)("("x+5")"))/color(red)cancel(color(black)(x+2)

This reduces the function to the line $y = x + 5$ with a removable discontinuity (a little hole in the graph) where $x = - 2$ and $y = - 2 + 5 = 3$.

So the hole is at (-2,3).

Step 2. Find the vertical asymptotes.

Since the denominator is now 1, there are no vertical asymptotes.

Step 3. Find the horizontal asymptotes.

This is a linear equation. There are no horizontal asymptotes.

There are no horizontal or vertical asymptotes.