24-12-2022 | 752
Với \(x \ne 3\) và \(x \ne -3\). Rút gọn biểu thức sau: \(A = \frac{5}{{x + 3}} + \frac{2}{{x - 3}} - \frac{{3{x^2} - 2x - 9}}{{{x^2} - 9}}\)
Bài làm
\(A = \frac{5}{{x + 3}} + \frac{2}{{x - 3}} - \frac{{3{x^2} - 2x - 9}}{{{x^2} - 9}}\)
\(= \frac{5}{{x + 3}} + \frac{2}{{x - 3}} - \frac{{3{x^2} - 2x - 9}}{{(x - 3)(x + 3)}}\)
\( = \frac{{5(x - 3)}}{{(x - 3)(x + 3)}} + \frac{{2(x + 3)}}{{(x - 3)(x + 3)}} - \frac{{3{x^2} - 2x - 9}}{{(x - 3)(x + 3)}}\)
\(= \frac{{5(x - 3) + 2(x + 3) - (3{x^2} - 2x - 9)}}{{(x - 3)(x + 3)}}\)
\(= \frac{{5x - 15 + 2x + 6 - 3{x^2} + 2x + 9}}{{(x - 3)(x + 3)}}\)
\(= \frac{{ - 3{x^2} + 9x}}{{(x - 3)(x + 3)}}\)
\(= \frac{{ - 3x(x - 3)}}{{(x - 3)(x + 3)}}\)
\(= \frac{{ - 3x}}{{x + 3}}\)
