Answer
The solution of the given equation is $\underline{\left( 1,7 \right)}$
Work Step by Step
We simplify the inequality further to obtain the value of x:
$\begin{align}
& \frac{x+5}{x-1}\gt2 \\
& x+5\gt2x-2 \\
& -x\gt-7 \\
& x\lt7
\end{align}$
For $ x=1$, $\frac{x+5}{x-1}$ is undefined as the denominator becomes zero.
To make the left hand side positive, the value of x should be greater than 1.
Hence, $x\gt1$
The solution of the given equation is $\underline{\left( 1,7 \right)}$
