# What are the excluded values of the function? y=\frac{5}{(6x-72)}

## Question:

What are the excluded values of the function?

{eq}\displaystyle y=\frac{5}{(6x-72)} {/eq}

## Rational Expression

A rational expression is a fraction where there numerator and/or denominator has an algebraic expression. It will become undefined when the value of the variable in the denominator makes the denominator equal to zero.

The given function is below:

{eq}\displaystyle y=\frac{5}{(6x-72)} {/eq}

It will become undefined when the denominator becomes zero. To determine the value of x that makes the expression undefined, the denominator has to be equated to zero and then solve for x:

{eq}6x-72 = 0 {/eq}

{eq}6x = 72 {/eq}

Dividing both sides by 6:

{eq}\displaystyle \frac{6x}{6} = \frac{72}{6} {/eq}

We get the value for x as:

{eq}x =12 {/eq}

To check we substitute that in the expression for the denominator:

{eq}6x-72 = 0 {/eq}

{eq}6(12)-72 = 0 {/eq}

{eq}72-72 = 0 {/eq}

Thus, the value {eq}x = 12 {/eq} does make the denominator equal to zero. This means that it has to be excluded because it will make the function undefined.