Question

[Lê Hồng Lam]

làm phép tính

\(\dfrac{x}{x^2+2xy}+\dfrac{1}{x-2y}+\dfrac{4y}{4y^2-x^2}\)

\(\dfrac{2x}{x-1}+\dfrac{5x^2-5}{x^2+2x+1}.\dfrac{2x+2}{5-5x}\)

\(\left(\dfrac{2x}{2x-1}+\dfrac{3x}{2x+1}\right).\dfrac{4x^2-4x+1}{8x^2+10x}\)

\(\dfrac{5x-5}{2x}.\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right)\)

GIÚP MÌNH VỚI CÁC BẠN

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(=\dfrac{1}{x+2y}+\dfrac{1}{x-2y}-\dfrac{4y}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{x-2y+x+2y-4y}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2\left(x-2y\right)}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2}{x+2y}\)

b: \(=\dfrac{2x}{x-1}+\dfrac{5\left(x-1\right)\left(x+1\right)}{\left(x+1\right)^2}\cdot\dfrac{2\left(x+1\right)}{5\left(1-x\right)}\)

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

c: \(=\dfrac{5\left(x-1\right)}{2x}\cdot\dfrac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{5\cdot4x}{2x\cdot\left(x+1\right)}=\dfrac{10}{x+1}\)