Answer
The required solution is $\frac{a\left( b+x \right)}{bx}$
Work Step by Step
We have the given expression $\frac{a}{x}+\frac{a}{b}=\frac{a}{x+b}$.
The left side of the given expression is
$\frac{a}{x}+\frac{a}{b}$
Simplify the above expression:
$\begin{align}
& \frac{a}{x}+\frac{a}{b}=\frac{a}{x}\times \frac{b}{b}+\frac{a}{b}\times \frac{x}{x} \\
& =\frac{ab}{xb}+\frac{ax}{bx} \\
& =\frac{ab+ax}{bx} \\
& =\frac{a\left( b+x \right)}{bx}
\end{align}$
And the right side of the given expression is
$\frac{a}{x+b}$
So, $\frac{a}{x}+\frac{a}{b}\ne \frac{a}{x+b}$
Thus, the correct form of the given equation is $\frac{a}{x}+\frac{a}{b}=$ $\frac{a\left( b+x \right)}{bx}$.
