Problem 88 - College Algebra Essentials

Question

Explain how to simplify a rational expression.

Step-by-Step Solution

Answer

By factoring the numerator and denominator and canceling out common factors, the rational expression \(\frac{24x^2}{48x}\) is simplified to \(x\).

Step 1: Identify the Rational Expression

Suppose the rational expression is \(\frac{24x^2}{48x}\). The goal is to simplify this expression to its least form.

Step 2: Factor the Numerator and Denominator

Start by factoring the numerator which is \(24x^2\). It can be factored into \(2*2*2*3*x*x\). Likewise, factor the denominator \(48x\) into \(2*2*2*2*3*x\). So, the rational expression becomes \(\frac{2*2*2*3*x*x}{2*2*2*2*3*x}\).

Step 3: Cancel Common Factors

In this step, you can cancel out the common factors in the numerator and denominator. In our case, \(2*2*2*3*x\) can be canceled out from both numerator and denominator. After canceling out, the rational expression will be \(\frac{2x}{2}\).

Step 4: Simplify the Left Factor

What is left is to simplify \(\frac{2x}{2}\) which will give \(x\).