[tex] \dfrac{ \frac{4}{4 - x} + \frac{5}{x - 4} }{ \frac{5}{x} + \frac{2}{x - 4} } = [/tex]
[tex] =\dfrac{ \frac{-4}{x - 4} + \frac{5}{x - 4} }{ \frac{5(x - 4)}{x(x - 4)} + \frac{2x}{x(x - 4)} } [/tex]
[tex] =\dfrac{ \frac{5-4}{x - 4} }{ \frac{5(x - 4) + 2x}{x(x - 4)} } [/tex]
[tex] =\dfrac{ \frac{1}{x - 4} }{ \frac{5x - 20 + 2x}{x(x - 4)} } [/tex]
[tex] =\dfrac{ \frac{1}{x - 4} }{ \frac{7x - 20}{x(x - 4)} } [/tex]
[tex] =\dfrac{1}{x - 4} \times \dfrac{x(x - 4)}{7x - 20} [/tex]
[tex] =\dfrac{x}{7x - 20} [/tex]
