Chapter 11.4, Problem 22MCQ

a.

To determine

To find the error in the given step to simplify

  $\frac{x-3}{x+4}\cdot \frac{x}{3-x}$

Answer to Problem 22MCQ

  $x-3\ne 3-x$

Explanation of Solution

Given:

First step in simplifying $\frac{x-3}{x+4}\cdot \frac{x}{3-x}$ is to divide out the common factor $x-3\text{ and }3-x$ .

Concept Used:

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

Calculation:

In order to find the error in the given step to simplify

  $\frac{x-3}{x+4}\cdot \frac{x}{3-x}$

When given first step in simplifying is to divide out the common factor $x-3\text{ and }3-x$ .

First, note that $x-3\text{ and }3-x$ , are not equal, i.e. they can’t be treated as common.

Since,

  $x-3\ne 3-x$

So first step can’t be to divide out the common factor $x-3\text{ and }3-x$ .

Thus, the error is:

  $x-3\ne 3-x$

b.

To determine

To tell the first step to in order to simplify

  $\frac{x-3}{x+4}\cdot \frac{x}{3-x}$

Answer to Problem 22MCQ

  $3-x=-\left(x-3\right)$

Explanation of Solution

Given:

  $\frac{x-3}{x+4}\cdot \frac{x}{3-x}$

Concept Used:

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

Calculation:

In order to tell the first step to in order to simplify

  $\frac{x-3}{x+4}\cdot \frac{x}{3-x}$

Put

  $3-x=-\left(x-3\right)$

So that numerator and denominator term will have a common factor to divide, as

  $\frac{x-3}{x+4}\cdot \frac{x}{3-x}=\frac{x-3}{x+4}\cdot \frac{x}{-\left(x-3\right)}$

Now, above can be further simplified by dividing the common factor $\left(x-3\right)$ .

Thus, first error should be to rewrite:

  $3-x=-\left(x-3\right)$