Problem 35 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 y-10}{3 y-15}$$

Step-by-Step Solution

Answer

The simplified form of the rational expression \(\frac{2y - 10}{3y - 15}\) is \(\frac{2}{3}\).

Step 1: Identify Common Factors in Numerator and Denominator

Examine both the numerator which is '2y - 10' and the denominator '3y - 15' for common factors. It's clear that both terms in the numerator can be divided by '2', and both terms in the denominator can be divided by '3'.

Step 2: Factor Out Common Factors

Factor out the common factors identified in Step 1 from the numerator and the denominator. Therefore, the expression is rewritten like this: \(\frac{2(y - 5)}{3(y - 5)}\).

Step 3: Cancel Common Factor from Numerator and Denominator

In this step, cancel out the common term '(y - 5)' from both the numerator and the denominator. This is in accordance with the simplification rule that a term in the numerator and the same term in the denominator cancels each other out to become 1.

Step 4: Write the Simplified Rational Expression

After simplifying, the rational number becomes \(\frac{2}{3}\). This is the most simplified form.