# What numbers for which the rational expression is undefined? \frac{8}{9x + 7}

## Question:

What numbers for which the rational expression is undefined?

{eq}\displaystyle \frac{8}{9x + 7} {/eq}

## Rational Expression:

A rational expression is a fraction where the numerator and the denominator are expressions of a variable. Since a fraction with a denominator 0 is not defined, a rational expression is undefined when its denominator is zero.

The given rational expression is:

$$\frac{8}{9x + 7}$$

A rational expression is undefined when its denominator is zero.

So we set the denominator to zero:

$$9x+7=0 \\ \text{Subtracting 7 from both sides}, \\ 9x =-7 \\ \text{Dividing both sides by 9}, \\ x= \dfrac{-7}{9}$$

Therefore, the given rational expression is NOT defined at {eq}\boxed{\mathbf{x= \dfrac{-7}{9}}} {/eq}.