Kết quả nào sau đây là sai?

28/38

\(\frac{{4{x^2} - 5z}}{{3xy}} + \frac{{4{x^2} + 5z}}{{3xy}} = \frac{{8x}}{{3y}}\);

\(\frac{{x + 3}}{{x - y}} + \frac{x}{{y - x}} - \frac{{x - 3}}{{x - y}} = \frac{{ - x + 6}}{{x - y}}\);

\[\frac{{3{a^2} - 5ab}}{{{a^2} - {b^2}}} + \frac{{2{a^2} - 4{b^2}}}{{{b^2} - {a^2}}} + \frac{{7ab - 3{b^2}}}{{{a^2} - {b^2}}} = \frac{{5a + 7b}}{{a + b}}\];

\(\frac{3}{{x + 3}} - \frac{{x - 6}}{{{x^2} + 3x}} = \frac{2}{x}\).

Giải thích

Đáp án đúng là: C

Ta có:

• \(\frac{{4{x^2} - 5z}}{{3xy}} + \frac{{4{x^2} + 5z}}{{3xy}} = \frac{{4{x^2} - 5z + 4{x^2} + 5z}}{{3xy}} = \frac{{8{x^2}}}{{3xy}} = \frac{{8x}}{{3y}}\);

• \(\frac{{x + 3}}{{x - y}} + \frac{x}{{y - x}} - \frac{{x - 3}}{{x - y}} = \frac{{x + 3 - x - x + 3}}{{x - y}} = \frac{{ - x + 6}}{{x - y}}\);

• \[\frac{{3{a^2} - 5ab}}{{{a^2} - {b^2}}} + \frac{{2{a^2} - 4{b^2}}}{{{b^2} - {a^2}}} + \frac{{7ab - 3{b^2}}}{{{a^2} - {b^2}}} = \frac{{3{a^2} - 5ab - 2{a^2} + 4{b^2} + 7ab - 3{b^2}}}{{{a^2} - {b^2}}}\]

\( = \frac{{{a^2} + 2ab + {b^2}}}{{{a^2} - {b^2}}} = \frac{{{{\left( {a + b} \right)}^2}}}{{\left( {a - b} \right)\left( {a + b} \right)}} = \frac{{a + b}}{{a - b}}\);

• \(\frac{3}{{x + 3}} - \frac{{x - 6}}{{{x^2} + 3x}} = \frac{{3x - x + 6}}{{x\left( {x + 3} \right)}} = \frac{{2x + 6}}{{x\left( {x + 3} \right)}} = \frac{{2\left( {x + 3} \right)}}{{x\left( {x + 3} \right)}} = \frac{2}{x}\).

Do đó phương án C là khẳng định sai.