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Chapter 7: Problem 95

Explain how to simplify a rational expression.

Short Answer

Expert verified
Simplify a rational expression by factoring the numerator and denominator, and then cancel out the common factors. The remaining fraction is the simplified rational expression.

Step by step solution

01

Factor the Numerator and Denominator

Write down the rational expression. Then, factor completely the polynomial in the numerator and the polynomial in the denominator. Factoring is breaking down the polynomials into their simplest components.
02

Cancel Common Factors

Now, cancel out any factors that are common to both the numerator and the denominator. These are factors that appear in both the numerator and denominator. This step simplifies the rational expression.
03

Write Down the Simplified Expression

After cancelling out the common factors, what's left is the simplified rational expression. Write it down, be aware that the answer may still be a fraction. It's simplified because it can't be factored or reduced any further.

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{y^{2}-6}{y^{2}+9 y+18}-\frac{y-4}{y+6}$$

Find \(b\) so that the solution of $$ \frac{7 x+4}{b}+13=x $$ is \(-6\)

Will help you prepare for the material covered in the first section of the next chapter. Evaluate \(5 x+7\) for \(x=a+h\)

Exercises \(100-102\) will help you prepare for the material covered in the next section. $$\text { Solve: } \frac{15}{8+x}=\frac{9}{8-x}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { The LCD of } \frac{1}{x} \text { and } \frac{2 x}{x-1} \text { is } x^{2}-1$$
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