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Chapter 0: Problem 15

Multiply or divide as indicated. $$\frac{x-2}{3 x+9} \cdot \frac{2 x+6}{2 x-4}$$

Short Answer

Expert verified
The result of the multiplication of the given fractions is \( \frac{2}{3} \).

Step by step solution

01

Simplify Each Fraction

Try to simplify each fraction. It can be observed that the denominator in the first fraction and the numerator in the second fraction can be factorized. Simplify them as follows:\[\frac{x-2}{3 (x+3)} \cdot \frac{2 (x+3)}{2 (x-2)}\]
02

Apply Multiplication Rule

Now, apply the multiplication rule for fractions, which is to multiply the numerators to get the new numerator and multiply the denominators to get the new denominator. The expression becomes:\[\frac{(x-2) \cdot 2 (x+3)}{3 (x+3) \cdot 2 (x-2)}\]
03

Simplify the Resulting Fraction

Finally, simplify the resulting fraction by cancelling common factors in the numerator and the denominator. The terms \((x-2)\) and \((x+3)\) can be cancelled which leads to the final simplified result:\[\frac{2}{3}\]

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