Problem 48 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x^{2}-14 x+49}{x^{2}-49}$$

Step-by-Step Solution

Answer

The simplified form of the rational expression is \(\frac{x-7}{x+7}\).

Step 1: Factor the Numerator

Factor the numerator \(x^{2}-14 x+49 = (x-7)^2\)

Step 2: Factor the Denominator

Factor the denominator \(x^{2}-49 = (x-7)(x+7)\)

Step 3: Simplify the Rational Expression

Cancel out the common factor of \((x-7)\) in the numerator and denominator to get \(\frac{x-7}{x+7}\)