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:

Loading...
Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4
4.9K

Related to this Question

Explore our homework questions and answers library