Giúp mình với!!!!!!!! Thực hiện các phép tính: $a)\frac{x^{3}+6x^{2}-25}{x^{3}+3x^{2}-10x}-$ $\frac{x+5}{2x-x^{2}}$ $b)\frac{9-3x}{x^{2}+5x+4}-$ $\frac{3x-23}{(1-x)(x+4)}$

Đáp án:

Giải thích các bước giải:

$\  a) \dfrac{x³ + 6x² - 25}{x³ + 3x² - 10x} - \dfrac{x + 5}{2x - x²} $

$\ = \dfrac{x³ + 6x² - 25}{x³ + 5x² - 2x² - 10x} + \dfrac{x + 5}{x² - 2x} $

$\ = \dfrac{x³ + 6x² - 25}{x(x - 2)(x + 5)} + \dfrac{x + 5}{x(x - 2)} $

$\ - ĐKXĐ: $ $\begin{cases} x\neq 0\\x-2\neq 0\\x+5\neq 0 \end{cases}$

$\ ⇒ $ $\begin{cases} x\neq 0\\x\neq 2\\x\neq -5 \end{cases}$

$\ ⇒ \dfrac{x³ + 6x² - 25}{x(x - 2)(x + 5)} + \dfrac{x + 5}{x(x - 2)} $

$\ = \dfrac{x³ + 6x² - 25}{x(x - 2)(x + 5)} + \dfrac{(x + 5)(x + 5)}{x(x - 2)(x + 5)} $ 

$\ = \dfrac{x³ + 6x² - 25}{x(x - 2)(x + 5)} + \dfrac{x² + 10x + 25}{x(x - 2)(x + 5)} $

$\ = \dfrac{x³ + 6x² - 25 + x² + 10x + 25}{x(x - 2)(x + 5)} $

$\ = \dfrac{x³ + 7x² + 10x}{x(x - 2)(x + 5)} $

$\ = \dfrac{x(x² + 7x + 10)}{x(x - 2)(x + 5)} $

$\ = \dfrac{x(x² + 5x + 2x + 10)}{x(x - 2)(x + 5)} $

$\ = \dfrac{x(x + 2)(x + 5)}{x(x - 2)(x + 5)} $

$\ = \dfrac{x + 2}{x - 2} $

$\ b) \dfrac{9 - 3x}{x² + 5x + 4} - \dfrac{3x - 23}{(1 - x)(x + 4)} $

$\ = \dfrac{9 - 3x}{x² + x + 4x+ 4} + \dfrac{3x - 23}{(x - 1)(x + 4)} $

$\ = \dfrac{9 - 3x}{(x + 1)(x + 4)} + \dfrac{3x - 23}{(x - 1)(x + 4)} $

$\ - ĐKXĐ: $ $\begin{cases} x+1\neq 0\\x-1\neq 0\\x+4\neq 0 \end{cases}$

$\ ⇒ $ $\begin{cases} x\neq -1\\x\neq 1\\x\neq -4 \end{cases}$

$\ ⇒ \dfrac{9 - 3x}{(x + 1)(x + 4)} + \dfrac{3x - 23}{(x - 1)(x + 4)} $

$\ = \dfrac{(9 - 3x)(x - 1)}{(x - 1)(x + 1)(x + 4)} + \dfrac{(3x - 23)(x + 1)}{(x + 1)(x - 1)(x + 4)} $

$\ = \dfrac{9x - 3x² - 9 + 3x}{(x - 1)(x + 1)(x + 4)}+ \dfrac{3x² - 23x + 3x - 23}{(x + 1)(x - 1)(x + 4)} $

$\ = \dfrac{9x - 3x² - 9 + 3x + 3x² - 23x + 3x - 23}{(x - 1)(x + 1)(x + 4)} $

$\ = \dfrac{- 8x - 32}{(x - 1)(x + 1)(x + 4)} $

$\ = \dfrac{- 8(x + 4)}{(x - 1)(x + 1)(x + 4)} $

$\ = \dfrac{- 8}{(x - 1)(x + 1)} $