Question

To multiply two rational expressions, we multiply their ___ together and multiply their ___ together. So the expression$\frac{2}{\left(x+1\right)}\cdot \frac{x}{x+3}$ is the same as ___ .

Short answer

To multiply two rational expressions, we multiply their numerator together and multiply their denominatortogether. So the expression$\frac{2}{x+1}\cdot \frac{x}{x+3}$ is the same as$\frac{2x}{\left(x+1\right)\left(x+3\right)}$

Step-by-step solution

Step 1. Apply the concept of multiplying rational expressions.

To multiply rational expressions, we use the following property of fractions:

$\frac{A}{B}\cdot \frac{C}{D}=\frac{AC}{BD}$

This says that to multiply two fractions, we multiply their numerators and multiply their denominators.

Step 2. Analyze the expression.

Given$\frac{2}{x+1}\cdot \frac{x}{x+3}$

This is a rational expression.

To multiply the rational expression, we use this property$\frac{A}{B}\cdot \frac{C}{D}=\frac{AC}{BD}$

Therefore, to multiply two rational expressions, we multiply their numerator together and multiply their denominator together.

Step 3. Simplify the expression.

Consider$\frac{2}{x+1}\cdot \frac{x}{x+3}$

We will multiply the numerators together and the denominators together:

$\frac{2}{x+1}\cdot \frac{x}{x+3}=\frac{2x}{\left(x+1\right)\left(x+3\right)}$