Bài `1`

`a)` $\dfrac{2x - 4}{5} + \dfrac{3x + 14}{5}$

$= \dfrac{2x - 4 + 3x + 14}{5}$

$= \dfrac{5x + 10}{5}$

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

$= x + 2$

`b)` $\dfrac{x + 1}{x - 5} + \dfrac{x - 18}{x - 5} + \dfrac{x + 2}{x - 5}$

$= \dfrac{x + 1 + x - 18 + x + 2}{x - 5}$

$= \dfrac{3x - 15}{x - 5}$

$= \dfrac{3(x - 5)}{x - 5}$

$= 3$

`c)` $\dfrac{2x^2 - x}{x - 1} + \dfrac{x + 1}{1 - x} + \dfrac{2 - x^2}{x - 1}$

$= \dfrac{2x^2 - x}{x - 1} - \dfrac{x + 1}{x - 1} + \dfrac{2 - x^2}{x - 1}$

$= \dfrac{2x^2 - x - x - 1 + 2 - x^2}{x - 1}$

$= \dfrac{x^2 - 2x + 1}{x - 1}$

$= \dfrac{(x - 1)^2}{x - 1}$

$= x - 1$

`d)` $\dfrac{2}{x + 1} - \dfrac{4}{1 - x} + \dfrac{5x + 1}{1 - x^2}$

$= \dfrac{2}{x + 1} + \dfrac{4}{x - 1} - \dfrac{5x + 1}{(x - 1)(x + 1)}$

$= \dfrac{2(x - 1) + 4(x + 1) - (5x + 1)}{(x - 1)(x + 1)}$

$= \dfrac{2x - 2 + 4x + 4 - 5x - 1}{(x - 1)(x + 1)}$

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

$= \dfrac{1}{x - 1}$

Bài `2`

`a)` $\dfrac{x^3 - 1}{x + 2} : (x^2 + x + 1)$

$= \dfrac{(x - 1)(x^2 + x + 1)}{x + 2} \cdot \dfrac{1}{x^2 + x + 1}$

$= \dfrac{x - 1}{x + 2}$

`b)` $\dfrac{x^4 + 2x^2 + 1}{x^2 - 2} \cdot \dfrac{x - 1}{2x + 2} \cdot \dfrac{2x^2 - 4}{(x^2 + 1)^2}$

$= \dfrac{(x^2 + 1)^2}{x^2 - 2} \cdot \dfrac{x - 1}{2(x + 1)} \cdot \dfrac{2(x^2 - 2)}{(x^2 + 1)^2}$

$= \dfrac{x - 1}{x + 1}$

`c)` $\dfrac{x^3 + 8}{x - 1} \cdot \dfrac{10 - 2x}{x + 2} + \dfrac{x^3 + 8}{x - 1} \cdot \dfrac{x - 9}{x + 2}$

$= \dfrac{x^3 + 8}{x - 1} \cdot \dfrac{1}{x + 2} \cdot (10 - 2x + x - 9)$

$= \dfrac{(x + 2)(x^2 - 2x + 4)}{(x - 1)(x + 2)} \cdot (1 - x)$

$= \dfrac{x^2 - 2x + 4}{x - 1} \cdot [-(x - 1)]$

$= -(x^2 - 2x + 4)$

`d)` $\dfrac{x^2 - 3x + 2}{x^2 - 5x + 6} \cdot \dfrac{x^2 - x - 6}{x^2 - 2x + 1}$

$= \dfrac{(x - 1)(x - 2)}{(x - 2)(x - 3)} \cdot \dfrac{(x - 3)(x + 2)}{(x - 1)^2}$

$= \dfrac{x - 1}{x - 3} \cdot \dfrac{(x - 3)(x + 2)}{(x - 1)^2}$

$= \dfrac{x + 2}{x - 1}$