Chapter 6.5, Problem 2ST

To determine

Find the missing numerator in the given expression.

Answer to Problem 2ST

The missing numerator is $5a$ .

Explanation of Solution

Given:

The given expression is $\frac{5}{1-a}=\frac{?}{a-a^2}$ .

Calculation:

Let the missing numerator $=m$

  $\frac{5}{1-a}=\frac{m}{a-a^2}$

Applycross multiplication.

  $\Rightarrow 5\left(a-a^2\right)=m\left(1-a\right)$

Divide both sides by $\left(1-a\right)$ .

  $\begin{array}{l}\Rightarrow \frac{5\left(a-a^2\right)}{\left(1-a\right)}=m\frac{\left(1-a\right)}{\left(1-a\right)}\\ \Rightarrow \frac{5a\left(1-a\right)}{\left(1-a\right)}=m\frac{\left(1-a\right)}{\left(1-a\right)}\\ \Rightarrow 5a=m\\ \Rightarrow m=5a\end{array}$

Hence the missing numeratoris $5a$ .