Question

[Mã Song]

Bt1: Thực hiện phép tính:

a/\(\left(\dfrac{2xy}{x^2-y^2}+\dfrac{x-y}{2x+2y}\right):\dfrac{x+y}{2x}+\dfrac{y}{y-x}\)

b/\(\left(\dfrac{x+2}{x+1}-\dfrac{2x}{x-1}\right)\)\(.\dfrac{3x+3}{x}+\dfrac{4x^2+x+7}{x^2-x}\)

c/\(\dfrac{1}{x^2+9x+20}+\dfrac{1}{x^2+11x+30}+\dfrac{1}{x^2+13x+42}\)

HELP ME!!!!!!!!! THỨ HAI MÌNH PHẢI KIỂM TRA RỒI

Answer 1

[Nguyễn Lê Phước Thịnh]

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

\(=\dfrac{x}{x-y}-\dfrac{y}{x-y}=1\)

b: \(=\dfrac{x^2+x-2-2x^2-2x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{3\left(x+1\right)}{x}+\dfrac{4x^2+x+7}{x\left(x-1\right)}\)

\(=\dfrac{-x^2-x-2}{\left(x-1\right)}\cdot\dfrac{3}{x}+\dfrac{4x^2+x+7}{x\left(x-1\right)}\)

\(=\dfrac{4x^2+x+7-3x^2-3x-6}{x\left(x-1\right)}=\dfrac{x^2-2x+1}{x\left(x-1\right)}=\dfrac{x-1}{x}\)

c: \(=\dfrac{1}{x+4}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+6}+\dfrac{1}{x+6}-\dfrac{1}{x+7}\)

\(=\dfrac{x+7-x-4}{\left(x+7\right)\left(x+4\right)}=\dfrac{3}{\left(x+4\right)\left(x+7\right)}\)