Problem 8 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{x-2}{x+9} \cdot \frac{5 x+45}{2 x-4}$$

Step-by-Step Solution

Answer

The result of the multiplication is \(\frac{5}{2}\).

Step 1: Simplify the Fractions

Each of the fractions can be simplified. The first fraction would remain the same while the second fraction can be simplified. For \(\frac{5x+45}{2x-4}\), take 5 out as a common factor from the numerator and 2 from the denominator. So it will be \(\frac{5(x+9)}{2(x-2)}\). Now our expression becomes, \(\frac{x-2}{x+9} \cdot \frac{5(x+9)}{2(x-2)}\).

Step 2: Multiply the Fractions

Multiply across as you would with simple fractions - multiply numerator with numerator and denominator with denominator. It's done this way: \(\frac{(x-2)\cdot 5(x+9)}{(x+9)\cdot 2(x-2)}\).

Step 3: Simplify the Result

Observe that both the numerator and the denominator of the equation have common factors, specifically (x-2) and (x+9). Therefore, we can simplify the equation by removing these common factors. The final result of the multiplication operation is \(\frac{5}{2}\).