Answer
The required solution is
$\frac{a+b}{ab}$
Work Step by Step
We have the given expression $\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b}$.
And the left-hand side of the given expression is
$\frac{1}{a}+\frac{1}{b}$
Simplify the above expression:
$\begin{align}
& \frac{1}{a}+\frac{1}{b}=\frac{1}{a}\times \frac{b}{b}+\frac{1}{b}\times \frac{a}{a} \\
& =\frac{b}{ab}+\frac{a}{ba} \\
& =\frac{b+a}{ab} \\
& =\frac{a+b}{ab}
\end{align}$
And the right-hand side of the given expression is
$\frac{1}{a+b}$
So, $\frac{1}{a}+\frac{1}{b}\ne \frac{1}{a+b}$.
Thus, the correct form of the given expression is $\frac{1}{a}+\frac{1}{b}=$ $\frac{a+b}{ab}$.
