Question

Simplify the rational expression.

$\frac{5\left(x-3\right)\left(2x+1\right)}{10{\left(x-3\right)}^2}$

Short answer

The simplified rational expression is$\frac{2x+1}{2\left(x-3\right)}$

Step-by-step solution

Step 1. Apply the concept of simplifying rational expressions.

To simplify rational expressions, we factor both numerator and denominator and use the following property of fractions:

$\frac{AC}{BC}=\frac{A}{B}$

This allows us to cancel common factors from the numerator and denominator.

Step 2. Analyze the expression.

Given$\frac{5\left(x-3\right)\left(2x+1\right)}{10{\left(x-3\right)}^2}$

This is a rational expression.

To simplify the rational expression, we factor both numerator and denominator and use this$\frac{AC}{BC}=\frac{A}{B}$

Therefore, to simplify a rational expression, we cancel factors that are common to the numerator and denominator.

Step 3. Simplify the expression.

Consider $\frac{5\left(x-3\right)\left(2x+1\right)}{10{\left(x-3\right)}^2}=\frac{5\left(x-3\right)\left(2x+1\right)}{5\cdot 2{\left(x-3\right)}^2}$

The common factor to the numerator and denominator is$5\left(x-3\right)$

So we will cancel the common factor from the numerator and denominator.

The simplified expression is$\frac{2x+1}{2\left(x-3\right)}$