Question

Bài 3: Thực hiện phép tính:

a) \(\frac{x^3 + 1}{x^2 + 2x + 1} \cdot \frac{x^2 - 1}{2x^2 - 2x + 2}\)

b) \(\frac{x-y}{xy+y^2} - \frac{3x+y}{x^2-xy} \cdot \frac{y-x}{x+y}\)

c) \(\frac{2x-2y}{x+y} : \frac{x^2-y^2}{xy} : \frac{x^2+2xy+y^2}{x}\)

Answer 1

a, `\frac{x^3+1}{x^2+2x+1}*\frac{x^2-1}{2x^2-2x+2}`

`=\frac{(x+1)(x^2-x+1)}{(x+1)^2}*\frac{(x-1)(x+1)}{2(x^2-x+1)}`

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

 

b, `\frac{x-y}{xy+y^2} - \frac{3x+y}{x^2-xy}* \frac{y-x}{x+y}`

`=\frac{x-y}{y(x+y)} + \frac{3x+y}{x(x-y)}* \frac{x-y}{x+y}`

`=\frac{x-y}{y(x+y)} + \frac{3x+y}{x(x+y)}`

`=\frac{x(x-y)}{xy(x+y)} + \frac{y(3x+y)}{xy(x+y)}`

`=\frac{x^2-xy+3xy+y^2}{xy(x+y)}`

`=\frac{x^2+2xy+y^2}{xy(x+y)}`

`=\frac{(x+y)^2}{xy(x+y)}`

`=\frac{x+y}{xy}`

 

c, `\frac{2x-2y}{x+y} : \frac{x^2 - y^2}{xy} * \frac{x^2+2xy+y^2}{x}`

`=\frac{2(x-y)}{x+y} * \frac{xy}{(x+y)(x-y)} * \frac{(x+y)^2}{x}`

`=2y`