Question

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

Answer 1

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+5color(blue)-color(blue)5=0color(blue)-color(blue)5`

`xcolor(red)cancelcolor(black)(color(black)+5color(blue)-color(blue)5)=0color(blue)-color(blue)5`

`x=0color(blue)-color(blue)5`

`x=-5`

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