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Chapter 0: Problem 16

Multiply or divide as indicated. $$\frac{6 x+9}{3 x-15} \cdot \frac{x-5}{4 x+6}$$

Short Answer

Expert verified
The answer is \( \frac{x + 3/2}{2x + 3} \)

Step by step solution

01

Simplify terms

The first task is to simplify the terms in each fraction as much as possible. In particular, the numerator and denominator of the first fraction, \( \frac{6x+9}{3x-15} \), can each be factored out by 3 to become \( \frac{2x+3}{x-5} \). Similarly, the numerator and denominator of the second fraction \( \frac{x-5}{4x+6} \) cannot be simplified
02

Cancel common factors

Next, look for common factors in the numerators and denominators across both fractions and cancel them out. Here, we can see that \(x - 5\) is a common factor in the numerator of the second fraction and the denominator of the first fraction, so we can cancel these out. Our expression thus becomes \( \frac{2x + 3}{4x + 6} \)
03

Simplify further

Again, simplify the terms as much as possible in the fraction. In this case, the numerator and the denominator have a common factor of 2. Therefore, the expression simplifies to \( \frac{x + 3/2}{2x + 3} \)

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