Questions: Question #4 Multiply the rational expressions. Write the product in simplest form, (20x+28)/(4x) * (2)/(35x+49)

Transcript text: Question \#4 Multiply the rational expressions. Write the product in simplest form, \[ \frac{20 x+28}{4 x} \cdot \frac{2}{35 x+49} \]

Solution

Solution Steps

To multiply the rational expressions, first factor each expression completely. Then, multiply the numerators together and the denominators together. Finally, simplify the resulting expression by canceling out any common factors.

Step 1: Factor the Expressions

First, we factor each part of the rational expressions. The expression \(\frac{20x + 28}{4x}\) can be factored as \(\frac{5x + 7}{x}\). The expression \(\frac{2}{35x + 49}\) can be factored as \(\frac{2}{7(5x + 7)}\).

Step 2: Multiply the Expressions

Next, we multiply the factored expressions: \[ \frac{5x + 7}{x} \cdot \frac{2}{7(5x + 7)} = \frac{2}{7x} \]

Step 3: Simplify the Product

The product \(\frac{2}{7x}\) is already in its simplest form, as there are no common factors to cancel out.