# How do you find the domain of f(x) = (x+3)/(2x-5)?

May 6, 2016

The domain is the set of all the $x -$values.
$x \epsilon \mathbb{R} , x \ne - \frac{5}{2}$

#### Explanation:

We have to decide if there are any values of $x$ which are invalid.

Looking at the numerator, $x + 3$, there is no problem or restriction for a value of $x$. The numerator can even be equal to 0

However, the denominator of a fraction may not be equal to 0.
If $2 x + 5 = 0$, then the value of $x$ is $- \frac{5}{2}$

So, for the domain, $x \epsilon \mathbb{R} , x \ne - \frac{5}{2}$

This reads as "$x$ may be any real number except $- \frac{5}{2}$.