Problem 34 - 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 simplified form of the expression \((x+4)/(x^{2}-16)\) is \(1/(x-4)\).

Step 1: 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 \((x+4)/[(x-4)*(x+4)]\).

Step 2: Cancel out the common factors

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