Với x khác+- 3. Rút gọn biểu thức sau: A = 5 / (x + 3) + 2 / (x - 3) - (3x^2 - 2x -9)
Giải thích
\(A = \frac{5}{{x + 3}} + \frac{2}{{x - 3}} - \frac{{3{x^2} - 2x - 9}}{{{x^2} - 9}}\)
\( = \frac{{5\left( {x - 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{{2\left( {x + 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} - \frac{{3{x^2} - 2x - 9}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\)
\( = \frac{{5x - 15 + 2x + 6 - 3{x^2} + 2x + 9}}{{\left( {x + 3} \right)\left( {x - 3} \right)}}\)
\( = \frac{{ - 3{x^2} + 9x}}{{\left( {x + 3} \right)\left( {x - 3} \right)}}\)\( = \frac{{ - 3x\left( {x - 3} \right)}}{{\left( {x + 3} \right)\left( {x - 3} \right)}} = \frac{{ - 3x}}{{x + 3}}\).