Question

Efraim wants to start simplifying the complex fraction$\frac{{\displaystyle \frac{1}{a}}+{\displaystyle \frac{1}{b}}}{{\displaystyle \frac{1}{a}}-{\displaystyle \frac{1}{b}}}$by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim’s plan.

Short answer

Simplified equation is :

$\frac{a+b}{b-a}$

Step-by-step solution

Step 1. Given information 

Efraim wants to start simplifying the complex fraction $\frac{{\displaystyle \frac{1}{a}+\frac{1}{b}}}{{\displaystyle \frac{1}{a}-\frac{1}{b}}}$

Step 2. Correct procedure

We can't cancel the term before taking the L.C.M of the term .

Hence the correct procedure is :

$$\begin{gathered} \frac{{\displaystyle \frac{1}{a}+\frac{1}{b}}}{{\displaystyle \frac{1}{a}-\frac{1}{b}}} \\ \frac{{\displaystyle \frac{b+a}{ab}}}{{\displaystyle \frac{b-a}{ab}}} \\ \frac{a+b}{b-a} \end{gathered}$$