Chapter 11.4, Problem 23MCQ

To determine

To explain the reason to simplify the for the first step taken by student to simplify the expression

  $\frac{7}{x}\cdot x^3$

Answer to Problem 23MCQ

So that the common factor x can be divided.

Explanation of Solution

Given:

First step in simplifying $\frac{7}{x}\cdot x^3$ is to rewrite it as $\frac{7}{x}\cdot \frac{x^3}{1}$ .

Concept Used:

An rational expression is simplified by dividing the common factor from denominator and numerator.

Calculation:

In order to explain the reason to simplify the for the first step taken by student to simplify the expression

  $\frac{7}{x}\cdot x^3$

When given first step taken is to rewrite it:

  $\frac{7}{x}\cdot x^3=\frac{7}{x}\cdot \frac{x^3}{1}$

First, note that to simplify an rational expression common factors from denominator and numerator should be divided. In the given expression $\frac{7}{x}\cdot x^3$ should be rewritten equals to $\frac{7}{x}\cdot \frac{x^3}{1}$ so that it can be seen that there is common factor x in denominator and numerator that can be divided out, as

  $\frac{7}{x}\cdot \frac{x^3}{1}=\frac{7}{1}\cdot \frac{x^2}{1}$

Thus, the reason to rewrite

  $\frac{7}{x}\cdot x^3=\frac{7}{x}\cdot \frac{x^3}{1}$ is so that the common factor x can be divided.