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Chapter 7: Problem 57

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

Short Answer

Expert verified
The given rational expression cannot be simplified further. So, the simplified form of the expression \(\frac{x+4}{x^{2}+16}\) remains the same.

Step by step solution

01

Analyzing the rational expression

Analyze the given expression \(\frac{x+4}{x^{2}+16}\). The numerator is \(x+4\) and the denominator is \(x^{2}+16\).
02

Factoring

Look for common factors within the numerator and the denominator. In this case, there don't seem to be any common factors that can be factored out on both the numerator and the denominator.
03

Checking reduction

Check if there are any reducible terms in the numerator and the denominator. The two terms of the denominator \(x^{2}+16\) can't be further simplified and they don't match any term in the numerator, and hence can't be reduced. Similarly, the numerator \(x+4\) can't be matched or reduced with any part of the denominator.

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