Problem 6 - Introductory Algebra for College Students

Question

Find the least common denominator of the rational expressions. $$\frac{2}{x-5} \text { and } \frac{3}{x+7}$$

Step-by-Step Solution

Answer

The least common denominator of the rational expressions \(\frac{2}{x-5}\) and \(\frac{3}{x+7}\) is \((x-5)*(x+7)\).

Step 1: Identify the Denominators

The denominators of the given rational expressions are \(x-5\) and \(x+7\).

Step 2: Compute the Least Common Multiple

The LCM is obtained by multiplying the denominators as they are different from each other and don't have any factors in common. So, the LCM of \(x-5\) and \(x+7\) is \((x-5)*(x+7)\).

Step 3: Write down the least common denominator

Hence, the least common denominator is \((x-5)*(x+7)\).