Answer
$\frac{9}{2}$
Work Step by Step
The value of x is calculated as follows.
$\begin{align}
& \frac{7}{{{x}^{2}}-5x}-\frac{2}{x-5}=\frac{4}{x} \\
& \frac{7-2x}{x\left( x-5 \right)}=\frac{4}{x} \\
& 7-2x=4\left( x-5 \right) \\
& 7-2x=4x-20
\end{align}$
$\begin{align}
& 4x+2x=7+20 \\
& 6x=27 \\
& x=\frac{27}{6} \\
& =\frac{9}{2}
\end{align}$
Check:
Substitute $\frac{9}{2}$ for $x$ in the given equation.
$\begin{align}
& \frac{7}{{{\left( \frac{9}{2} \right)}^{2}}-5\left( \frac{9}{2} \right)}-\frac{2}{\left( \frac{9}{2} \right)-5}=\frac{4}{\left( \frac{9}{2} \right)} \\
& \frac{7}{\left( \frac{81}{4}-\frac{45}{2} \right)}-\frac{2}{\left( \frac{9-10}{2} \right)}=\frac{8}{9} \\
& \frac{7}{\left( \frac{81-90}{4} \right)}-\frac{2}{\left( \frac{9-10}{2} \right)}=\frac{8}{9} \\
\end{align}$
Simplify further,
$\begin{align}
\frac{28}{-9}-\frac{4}{-1}\overset{?}{\mathop{=}}\,\frac{8}{9} & \\
\frac{28-36}{-9}\overset{?}{\mathop{=}}\,\frac{8}{9} & \\
\frac{-8}{-9}\overset{?}{\mathop{=}}\,\frac{8}{9} & \\
\frac{8}{9}\overset{?}{\mathop{=}}\,\frac{8}{9} & \\
\end{align}$
