\(A = \left( {\frac{{x - 3}}{x} - \frac{x}{{x - 3...

B

- Hướng dẫn giải

Phương pháp giải:

Áp dụng công thức: \(\frac{A}{B}:\frac{C}{D} = \frac{A}{B}.\frac{D}{C} = \frac{{A.D}}{{B.C}}\)

Giải chi tiết:

\(\begin{array}{l}\,A = \left( {\frac{{x - 3}}{x} - \frac{x}{{x - 3}} + \frac{9}{{{x^2} - 3x}}} \right):\frac{{2x - 2}}{x}\\\,\,\,\,\,\,A = \left( {\frac{{{{(x - 3)}^2}}}{{x(x - 3)}} - \frac{{x.x}}{{x - 3}} + \frac{9}{{{x^2} - 3x}}} \right) \cdot \frac{x}{{2x - 2}}\\\,\,\,\,\,\,A = \left( {\frac{{{{(x - 3)}^2} - {x^2} + 9}}{{x(x - 3)}}} \right) \cdot \frac{x}{{2(x - 1)}}\\\,\,\,\,\,\,A = \frac{{{x^2} - 6x + 9 - {x^2} + 9}}{{x(x - 3)}} \cdot \frac{x}{{2(x - 1)}}\\\,\,\,\,\,A = \frac{{ - 6x + 18}}{{x(x - 3)}} \cdot \frac{x}{{2(x - 1)}} = \frac{{ - 6(x - 3)x}}{{x(x - 3).2.(x - 1)}} = \frac{{ - 3}}{{x - 1}}\end{array}\)