Incorrect. Because $\displaystyle{{x}}^{{2}}-{1}={\left({x}+{1}\right)}{\left({x}-{1}\right)}\usepackage{cmbright}\Huge\$ , you should multiply both sides of the equation by $\displaystyle{\left({x}+{1}\right)}{\left({x}-{1}\right)}\usepackage{cmbright}\Huge\$ to clear the denominators:

$\displaystyle\frac{{{5}{x}{\left({{x}}^{{2}}-{1}\right)}}}{{{{x}}^{{2}}-{1}}}=\frac{{{4}{\left({x}+{1}\right)}{\left({x}-{1}\right)}}}{{{x}-{1}}}-\frac{{{2}{\left({x}+{1}\right)}{\left({x}-{1}\right)}}}{{{x}+{1}}}\usepackage{cmbright}\Huge\$

Simplify to get a linear equation. Combine like terms and solve for x.