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91Ó°ÊÓ

In the following exercises, solve each rational function inequality and write the solution in interval notation.

Given the function,

R(x)=x+1x+3, find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

The values of x: (-3,-1]

Step by step solution

01

Step 1. Given information.

The given function isR(x)=x+1x+3.

02

Step 2. Write the inequality. 

According to the given condition, the function will be greater than or equal to 0.

So,

x+1x+3≤0

03

Step 3. Solve the rational inequality for x. 

Let's solve the inequality for x.

Here, x+1x+3≤0

Solve this inequality. We will get

x>-3orx≤-1

In interval notation;

(-3,-1]

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