Problem 13 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{4 y+30}{y^{2}-3 y} \cdot \frac{y-3}{2 y+15}$$

Step-by-Step Solution

Answer

The simplified multiplication of the given expressions is \( \frac{2}{y(y+5)} \)

Step 1: Factor the Fractions

Factor the given fractions. This gives \( \frac{2(2y+15)}{y(y-3)} \cdot \frac{y-3}{y+5} \)

Step 2: Cancel terms

Upon factoring, you notice that (2y+15) and (y-3) are terms in both the numerator and the denominator. You can cancel them out, simplify if possible, and write the simplest form of the fractions.

Step 3: Perform the Multiplication

After cancelling out like terms, the resulting fractions are \( \frac{2}{y} \cdot \frac{1}{y+5} \). Multiply the numerators and the denominators separately. Multiply 2 by 1 for the numerator, and y by (y+5) for the denominator. The multiplication yields \( \frac{2}{y(y+5)} \)