# Simplify and find the excluded values. \frac{15x^2}{15x + 10}

## Question:

Simplify and find the excluded values.

{eq}\displaystyle \frac{15x^2}{15x + 10} {/eq}

## Rational Expression:

A rational expression is a fraction where the numerator and the denominator are the expressions of a variable. A rational expression is undefined when its denominator is zero.

## Answer and Explanation:

The given expression is:

\begin{align} \frac{15x^2}{15x + 10}&= \dfrac{5(3x^2)}{5(3x+2)} \\ &= \dfrac{3x^2}{3x+2} & \text{(5 is canceled)} \end{align}

A rational expression is undefined when its denominator is zero.

So to find the excluded values, we set the denominator to zero.

$$3x+2=0 \\ \text{Subtracting 1 from both sides}, \\ 3x =-2 \\ \text{Dividing both sides by 3}, \\ x= \dfrac{-2}{3}$$

Therefore, the simplified form of the given expression is: {eq}\boxed{\mathbf{ \dfrac{3x^2}{3x+2}}} {/eq} and the excluded value is {eq}\boxed{\mathbf{ \dfrac{-2}{3} }} {/eq}.

#### Learn more about this topic:

Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4
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