rút gọn hộ mik vs x/x ²-5x+6-2/2-x+x/x-3 06/12/2021 Bởi Madeline rút gọn hộ mik vs x/x ²-5x+6-2/2-x+x/x-3
$\frac{x}{x^{2}-5x+6}-$ $\frac{2}{2-x}+$ $\frac{x}{x-3}$ =$\frac{x}{x^{2}-5x+6}+$ $\frac{2(x-3)}{(x-2)(x-3)}+$ $\frac{x(x-2)}{(x-2)(x-3)}$ =$\frac{x}{x^{2}-5x+6}+$ $\frac{2x-6}{x^{2}-5x+6}+$ $\frac{x^{2}-2x}{x^{2}-5x+6}$ =$\frac{x+2x-6+x^{2}-2x}{x^{2}-5x+6}$ =$\frac{x^{2}+x-6}{x^{2}-5x+6}$ =$\frac{(x-2)(x+3)}{(x-2)(x-3)}$ =$\frac{x+3}{x-3}$ Bình luận
Đáp án: $\dfrac{x+3}{x-3}$ Giải thích các bước giải: $\begin{array}{l}\dfrac{x}{x^2- 5x + 6} – \dfrac{2}{2-x} + \dfrac{x}{x-3}\qquad (x \ne 2;\, x \ne 3)\\ = \dfrac{x}{(x-2)(x-3)} + \dfrac{2(x-3)}{(x-2)(x-3)} + \dfrac{x(x-2)}{(x-2)(x-3)}\\ = \dfrac{x +2x – 6 + x^2 – 2x}{(x-2)(x-3)}\\ = \dfrac{x^2 + x – 6}{(x-2)(x-3)} \\ = \dfrac{(x-2)(x+3)}{(x-2)(x-3)}\\ = \dfrac{x+3}{x-3}\end{array}$ Bình luận
$\frac{x}{x^{2}-5x+6}-$ $\frac{2}{2-x}+$ $\frac{x}{x-3}$
=$\frac{x}{x^{2}-5x+6}+$ $\frac{2(x-3)}{(x-2)(x-3)}+$ $\frac{x(x-2)}{(x-2)(x-3)}$
=$\frac{x}{x^{2}-5x+6}+$ $\frac{2x-6}{x^{2}-5x+6}+$ $\frac{x^{2}-2x}{x^{2}-5x+6}$
=$\frac{x+2x-6+x^{2}-2x}{x^{2}-5x+6}$
=$\frac{x^{2}+x-6}{x^{2}-5x+6}$
=$\frac{(x-2)(x+3)}{(x-2)(x-3)}$
=$\frac{x+3}{x-3}$
Đáp án:
$\dfrac{x+3}{x-3}$
Giải thích các bước giải:
$\begin{array}{l}\dfrac{x}{x^2- 5x + 6} – \dfrac{2}{2-x} + \dfrac{x}{x-3}\qquad (x \ne 2;\, x \ne 3)\\ = \dfrac{x}{(x-2)(x-3)} + \dfrac{2(x-3)}{(x-2)(x-3)} + \dfrac{x(x-2)}{(x-2)(x-3)}\\ = \dfrac{x +2x – 6 + x^2 – 2x}{(x-2)(x-3)}\\ = \dfrac{x^2 + x – 6}{(x-2)(x-3)} \\ = \dfrac{(x-2)(x+3)}{(x-2)(x-3)}\\ = \dfrac{x+3}{x-3}\end{array}$