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Chapter 7: Problem 34

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x+4}{x^{2}-16}$$

Short Answer

Expert verified
The simplified form of the expression \((x+4)/(x^{2}-16)\) is \(1/(x-4)\).

Step by step solution

01

Factorize the denominator

Rewrite the denominator \(x^{2}-16\) as difference of squares. This results in \((x-4)*(x+4)\). The whole expression then becomes \((x+4)/[(x-4)*(x+4)]\).
02

Cancel out the common factors

Cancel the common factor \(x+4\) of the numerator and the denominator. This leaves us with \(1/(x-4)\).

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Most popular questions from this chapter

What are similar triangles?

What is a proportion? Give an example with your description.

perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x-1}{x^{2}+5 x-6}-\frac{2 x-7}{x^{2}+5 x-6}\right) \div \frac{x+2}{x^{2}-1}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+3}{2}+\frac{x+5}{4}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$
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