Chapter A.3, Problem 21E

Solution

Find the missing numerator or denominator so that the two rational expressions are equal.

  $x^2$ .

Given:

The given rational expression is $\frac{x-4}{x}=\frac{x^2-4x}{?}$ .

Calculation:

The given rational expression is $\frac{x-4}{x}=\frac{x^2-4x}{?}$ .

As given the two rational expressions are equal.

  $\begin{array}{c}\frac{x-4}{x}=\frac{x^2-4x}{?}\\ \frac{x-4}{x(x^2-4x)}=\frac{1}{?}\\ \frac{(x-4)}{x\cdot x(x-4)}=\frac{1}{?}\\ \frac{1}{x^2}=\frac{1}{?}\\ ?=x^2\end{array}$

So the rational expression will be $\frac{x-4}{x}=\frac{x^2-4x}{x^2}$ .

Thus the missing denominator (?) is = $x^2$ .