Problem 57 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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 1: Analyzing the rational expression

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

Step 2: 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.

Step 3: 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.