Problem 36 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{6 y+18}{11 y+33}$$

Step-by-Step Solution

Answer

The simplified form of \(\frac{6y + 18}{11y + 33}\) is \(\frac{6}{11}\)

Step 1: Factor out common term from numerator and denominator

First, look for a common term in the numerator and denominator of the given expression. In the numerator, \(6 y + 18\), the common term is 6. After factoring out 6, the numerator becomes \(6(y + 3)\). In the denominator, \(11 y + 33\), the common term is 11. After factoring out 11, the denominator becomes \(11(y + 3)\). Therefore, the rational expression is now written as \(\frac{6(y + 3)}{11(y + 3)}\).

Step 2: Simplify the expression

Notice that \(y + 3\) is a common factor in the numerator and the denominator. Cancelling out this common factor, the simplified rational expression becomes: \(\frac{6}{11}\)