Problem 8 - Introductory Algebra for College Students

Question

Find the least common denominator of the rational expressions. $$\frac{8}{11(y+5)} \text { and } \frac{12}{y}$$

Step-by-Step Solution

Answer

The LCD is \(11*y*(y+5)\).

Step 1: Understand the problem

The problem is asking for the least common denominator (LCD) of \(\frac{8}{11(y+5)}\) and \(\frac{12}{y}\). This is the least common multiple of the two denominators \(y\) and \(11(y+5)\).

Step 2: Break down the denominators

Note that the denominator of the first fraction is \(11(y+5)\) and the denominator of the second fraction is \(y\).

Step 3: Finding the Least Common Multiple (LCM)

In the case of variables, the LCM is usually the product of the highest powers of all primes appearing in the factors, in this case simply \(y\) and \(11(y+5)\). So, the least common denominator is \(11*y*(y+5)\).