# What are the excluded values for y=(2x+5)/(x+5)?

Mar 31, 2018

The only excluded value is $x = - 5$.

#### Explanation:

Excluded values occur when the denominator of a fraction equals zero.

In simpler terms, excluded fractions are when $x$ makes it so that the bottom of the fraction is $0$.

This is because division by zero is not possible, so the value of $x$ is excluded.

To solve for the excluded variable, simply take the denominator, set it equal to $0$, then solve for $x$. That will tell you what value of $x$ will make the denominator $0$.

Here's what that looks like:

$x + 5 = 0$

$x + 5 \textcolor{b l u e}{-} \textcolor{b l u e}{5} = 0 \textcolor{b l u e}{-} \textcolor{b l u e}{5}$

$x \textcolor{red}{\cancel{\textcolor{b l a c k}{\textcolor{b l a c k}{+} 5 \textcolor{b l u e}{-} \textcolor{b l u e}{5}}}} = 0 \textcolor{b l u e}{-} \textcolor{b l u e}{5}$

$x = 0 \textcolor{b l u e}{-} \textcolor{b l u e}{5}$

$x = - 5$

This is the excluded value for $x$. Hope this helped!