# What is the domain of 3/(5-7x)?

May 14, 2018

$\left(- \infty , \frac{5}{7}\right) \cup \left(\frac{5}{7} , \infty\right)$

#### Explanation:

The denominator of the rational expression cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

$\text{solve "5-7x=0rArrx=5/7larrcolor(red)"excluded value}$

$\text{domain is } x \in \left(- \infty , \frac{5}{7}\right) \cup \left(\frac{7}{5} , \infty\right)$

$\text{note that the curved brackets " ( )" indicate that x cannot }$
$\text{equal these values but can equal the values between them}$
graph{3/(5-7x) [-10, 10, -5, 5]}