Answer
The required solution is
$\frac{7x+1}{x}$
Work Step by Step
We have the given expression $\frac{1}{x}+7=\frac{1}{x+7}$.
The left side of the given expression is
$\frac{1}{x}+7$
And we simplify the above expression:
$\begin{align}
& \frac{1}{x}+7=\frac{1}{x}+7\times \frac{x}{x} \\
& =\frac{1}{x}+\frac{7x}{x} \\
& =\frac{1+7x}{x} \\
& =\frac{7x+1}{x}
\end{align}$
So, the right side of the given expression is
$\frac{1}{x+7}$
So, $\frac{1}{x}+7\ne \frac{1}{x+7}$.
Thus, the correct form of the given equation is $\frac{1}{x}+7=$ $\frac{7x+1}{x}$.
