Làm giúp mình bài4 nhé

Bài `4.`

`a)`

ĐKXĐ: `x \ne -23` và `x \ne 1`

`\frac{2x}{x + 23} \cdot \frac{3x}{x - 1} + \frac{2x}{x + 23} \cdot \frac{23 - 2x}{x - 1}`

`= \frac{2x}{x + 23}.( \frac{3x}{x - 1} + \frac{23 - 2x}{x - 1})`

`= \frac{2x}{x + 23} \cdot ( \frac{3x + 23 - 2x}{x - 1})`

`= \frac{2x}{x + 23} \cdot \frac{x + 23}{x - 1}`

`= \frac{2x}{x - 1}`

`---`

`b)`

ĐKXĐ: `x \ne 2, x \ne -1, y \ne -6`

`\frac{y + 6}{x^2 - 4x + 4} \cdot \frac{x^2 - 4}{x + 1} \cdot \frac{x - 2}{y + 6}`

`= \frac{y + 6}{(x - 2)^2} \cdot \frac{(x - 2)(x + 2)}{x + 1} \cdot \frac{x - 2}{y + 6}`

`= \frac{(y + 6) \cdot (x - 2) \cdot (x + 2) \cdot (x - 2)}{(x - 2)^2 \cdot (x + 1) \cdot (y + 6)}` 

`= \frac{x + 2}{x + 1}`

`---`

`c)`

ĐKXĐ: `x \ne -1975` và `x \ne -1945`

`\frac{19x + 8}{x + 1975} \cdot \frac{2000 - x}{x + 1945} + \frac{19x + 8}{x + 1975} \cdot \frac{2x - 25}{x + 1945}`

`= \frac{19x + 8}{x + 1975}.( \frac{2000 - x}{x + 1945} + \frac{2x - 25}{x + 1945})`

`= \frac{19x + 8}{x + 1975} \cdot ( \frac{2000 - x + 2x - 25}{x + 1945})`

`= \frac{19x + 8}{x + 1975} \cdot \frac{x + 1975}{x + 1945}`

`= \frac{19x + 8}{x + 1945}`

`---`

`d)`

ĐKXĐ: `x \ne 7` và `x \ne -7`

`(x ^ 2 - 49)/(x ^ 2 + 5) . ((x ^ 2 + 5)/(x - 7) - (x ^ 2 + 5)/(x + 7))`

`= \frac{x^2 - 49}{x^2 + 5} \cdot (x^2 + 5)( \frac{1}{x - 7} - \frac{1}{x + 7})`

`= (x^2 - 49) \cdot( \frac{x + 7 - (x - 7)}{(x - 7)(x + 7)})`

`= (x^2 - 49) \cdot \frac{14}{x^2 - 49}`

`= 14`