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Chapter 7: Problem 63

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x-5}{x+5}$$

Short Answer

Expert verified
\(\frac{x-5}{x+5}\)

Step by step solution

01

Identify any common factors

In the given expression, \(\frac{x-5}{x+5}\), the numerator is \(x-5\) and the denominator is \(x+5\). There are no common factors in the numerator and the denominator that we can cancel out.
02

Check if the numerator and the denominator are factorable

The numerator \(x-5\) and the denominator \(x+5\) can not be factored any further. Therefore, we can't simplify this expression any further.
03

Write the final solution

Since there are no common factors in the numerator and denominator to cancel out and the numerator and denominator are not factorable, the expression is already simplified. So, the simplified form of the given expression \(\frac{x-5}{x+5}\) is \(\frac{x-5}{x+5}\).

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Most popular questions from this chapter

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{3 x+6}{2}-\frac{x}{2}=x+3$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4-x}{x-9}-\frac{3 x-8}{9-x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-7}{y^{2}-16}+\frac{7-y}{16-y^{2}}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{b}{a c+a d-b c-b d}-\frac{a}{a c+a d-b c-b d}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{3 x}{(x+1)^{2}}-\left[\frac{5 x+1}{(x+1)^{2}}-\frac{3 x+2}{(x+1)^{2}}\right]$$
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