Solve for: (\frac{x-4)/(x-2)-5/x}{3/x+1}

Expression: $\frac{\frac{x-4}{x-2}-\frac{5}{x}}{\frac{3}{x}+1}$

Join $\frac{x-4}{x-2}-\frac{5}{x}:{\quad}\frac{x^{2}-9x+10}{x(x-2)}$

$=\frac{\frac{x^{2}-9x+10}{x(x-2)}}{\frac{3}{x}+1}$

Join $\frac{3}{x}+1:{\quad}\frac{x+3}{x}$

$=\frac{\frac{x^{2}-9x+10}{x(x-2)}}{\frac{x+3}{x}}$

Apply the fraction rule $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}$

$=\frac{(x^{2}-9x+10)x}{x(x-2)(x+3)}$

Cancel the common factor: $ x$

$=\frac{x^{2}-9x+10}{(x-2)(x+3)}$