Giải bài 5 trang 22

Tính: a) x−2x−y4+x+4y12x−2x−y4+x+4y12x - \frac{{2x - y}}{4} + \frac{{x + 4y}}{{12}};

Đề bài

Tính:

a) $x - \frac{2 x - y}{4} + \frac{x + 4 y}{12}$ ;

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

c) $\frac{4}{x + 2} - \frac{3}{x - 2} + \frac{12}{x^{2} - 4}$ ;

d) $\frac{x + y}{x^{2} - x y} - \frac{4 x}{x^{2} - y^{2}} - \frac{x - y}{x^{2} + x y}$ .

Phương pháp giải - Xem chi tiết

Tính:

a) $x - \frac{2 x - y}{4} + \frac{x + 4 y}{12}$ ;

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

c) $\frac{4}{x + 2} - \frac{3}{x - 2} + \frac{12}{x^{2} - 4}$ ;

d) $\frac{x + y}{x^{2} - x y} - \frac{4 x}{x^{2} - y^{2}} - \frac{x - y}{x^{2} + x y}$ .

Lời giải chi tiết

a) $x - \frac{2 x - y}{4} + \frac{x + 4 y}{12} = \frac{12 x}{12} - \frac{3 (2 x - y)}{12} + \frac{x + 4 y}{12} = \frac{12 x - 6 x + 3 y + x + 4 y}{12} = \frac{7 x + 7 y}{12}$

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

c) $\frac{4}{x + 2} - \frac{3}{x - 2} + \frac{12}{x^{2} - 4} = \frac{4 (x - 2)}{(x + 2) (x - 2)} - \frac{3 (x + 2)}{(x + 2) (x - 2)} + \frac{12}{(x + 2) (x - 2)}$

$= \frac{4 x - 8 - 3 x - 6 + 12}{(x + 2) (x - 2)} = \frac{x - 2}{(x + 2) (x - 2)} = \frac{1}{x + 2}$

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

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