Chapter A.3, Problem 22E

Solution

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

  $x^2-2x$ .

Given:

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

Calculation:

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

As given the two rational expressions are equal.

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

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

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