Question

Which expression is equivalent to the following complex fraction 3/x-1 - 4 divided by 2 - 2/x-1

Answer 1

$\bf \cfrac{\quad \frac{3}{x-1}-4\quad }{2-\frac{2}{x-1}}\implies \cfrac{\quad \frac{3-4(x-1)}{x-1}\quad }{\frac{2(x-1)-2}{x-1}}\implies \cfrac{\quad \frac{3-4x+4}{x-1}\quad }{\frac{2x-2-2}{x-1}}\implies \cfrac{\quad \frac{7-4x}{x-1}\quad }{\frac{2x-4}{x-1}} \\\\\\ \cfrac{7-4x}{\underline{x-1}}\cdot \cfrac{\underline{x-1}}{2x-4}\implies \cfrac{7-4x}{2x-4}\implies \cfrac{-4x+7}{2(x-2)}$