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Thực hiện các phép cộng, trừ phân thức sau: x/x+2 - x/x-2

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Giải SBT Toán 8 Bài 6: Cộng, trừ phân thức

a) $\frac{x}{x + 2} - \frac{x}{x - 2}$ ;

b) $\frac{3 x}{2 y} + \frac{5 x}{3 y}$ ;

c) $\frac{y - 1}{5 y} - \frac{3 x - 1}{15 x}$ ;

d) $\frac{1 - x}{x^{3}} + \frac{1}{x^{2}}$ ;

e) $\frac{x - 2 y}{x y^{2}} - \frac{y - 2 x}{x^{2} y}$ ;

g) $\frac{1 - y^{2}}{3 x y} + \frac{2 y^{3} - 1}{6 x y^{2}}$ .

a) $\frac{x}{x + 2} - \frac{x}{x - 2} = \frac{x (x - 2)}{(x + 2) (x - 2)} - \frac{x (x + 2)}{(x + 2) (x - 2)}$

$= \frac{x^{2} - 2 x - x^{2} - 2 x}{(x + 2) (x - 2)} = \frac{- 4 x}{(x + 2) (x - 2)}$ .

b) $\frac{3 x}{2 y} + \frac{5 x}{3 y} = \frac{3 x . 3}{2 y . 3} + \frac{5 x . 2}{3 y . 2} = \frac{9 x + 10 x}{6 y} = \frac{19 x}{6 y}$ .

c) $\frac{y - 1}{5 y} - \frac{3 x - 1}{15 x} = \frac{(y - 1) . 3 x}{5 y . 3 x} - \frac{(3 x - 1) . y}{15 x . y}$

$= \frac{3 x y - 3 x - (3 x y - y)}{15 x y} = \frac{3 x y - 3 x - 3 x y + y}{15 x y} = \frac{y - 3 x}{15 x y}$ .

d) $\frac{1 - x}{x^{3}} + \frac{1}{x^{2}} = \frac{1 - x}{x^{3}} + \frac{1 . x}{x^{2} . x} = \frac{1 - x + x}{x^{3}} = \frac{1}{x^{3}}$ .

e) $\frac{x - 2 y}{x y^{2}} - \frac{y - 2 x}{x^{2} y} = \frac{(x - 2 y) . x}{x y^{2} . x} - \frac{(y - 2 x) . y}{x^{2} y . y}$

$= \frac{x^{2} - 2 x y - y^{2} + 2 x y}{x^{2} y^{2}} = \frac{x^{2} - y^{2}}{x^{2} y^{2}}$ .

g) $\frac{1 - y^{2}}{3 x y} + \frac{2 y^{3} - 1}{6 x y^{2}} = \frac{(1 - y^{2}) . 2 y}{3 x y . 2 y} + \frac{2 y^{3} - 1}{6 x y^{2}}$

$= \frac{2 y - 2 y^{3} + 2 y^{3} - 1}{6 x y^{2}} = \frac{2 y - 1}{6 x y^{2}}$ .