B1: Rút gọn A=\(\left(\frac{x}{x-1}-\frac{1}{x^2}\right):\left(\frac{1}{x+1}+\frac{2}{x^2-1}\right)\)

B2: Rút gọn A=\(\left(\frac{x-y}{x+y}-\frac{x+y}{x-y}\right):\frac{-4y^2}{x-y}\)

Rút gọn : B = (x² - 1)\(\left(\frac{1}{x-1}-\frac{1}{x+1}-1\right)\) 

               C = \(\left(y\frac{x^2+y^2}{x+y}\right).\left(\frac{2y}{x}-\frac{4y}{x-y}\right)\)

Rút gọn: \(\left(\frac{x-y}{y}+\frac{4x}{x+y}\right)\left(1+\frac{y+1}{x}+\frac{y}{^{x^2}}\right)\left(\frac{x^2+y^2}{2x^2y}\right)^{-1}\) biết CT: \(x^{-1}=\frac{1}{x}\)hoặc \(\left(\frac{A}{B}\right)^{-1}=\frac{B}{A}\)

Rút gọn : \(H=\frac{x^2y^2}{\left(x+1\right)\left(y-1\right)}+\frac{x^2}{\left(x+y\right)\left(y-1\right)}+\frac{y^2}{\left(x+1\right)\left(x+y\right)}\)

Bài 1 rút gọn biểu thức 

A=\(\left(x-\frac{4xy}{x+y}+y\right)\):\(\left(\frac{x}{x+y}-\frac{y}{x-y}-\frac{2xy}{x^2-y^2}\right)\)

B=\(\left(\frac{x-y}{2y-x}-\frac{x^2+y^2+y-2}{x^2-xy-2y^2}\right)\):\(\left(\frac{x^2+4x^2y^2+y^4}{x^2+y+xy+x}\right):\left(\frac{1}{2x^2+y+2}\right)\)

cm các biểu thức sau ko phụ thuộc vào biến:

a,\(\left[\frac{2\left(x+1\right)\left(y+1\right)}{\left(x+1\right)^2-\left(y+1\right)^2}+\frac{x-y}{2x+2y+4}\right].\frac{2x+2}{x+y+2}+\frac{y+1}{y-x}\)

b,\(\left[2\left(x+y\right)+1-\frac{1}{1-2x-2y}\right]:\left[2x+2y-\frac{4x^2+8xy+4y^2}{2x+2y-1}\right]+2\left(x+y\right)\)

Cho P= \(\frac{x^2}{\left(x+y\right)\left(1-y\right)}-\frac{y^2}{\left(x+y\right)\left(1+x\right)}-\frac{x^2y^2}{\left(1+x\right)\left(1-y\right)}\)

a) tìm đkxđ, rút gọn P

b)Tìm x,y t/m phg trình P=2

Câu 21:

\(\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}\right)+\frac{1}{4}\left(x^{16}+y^{16}\right)-\left(1+x^2y^2\right)^2\ge x^4y^4+\frac{x^8y^8}{2}-1-2x^2y^2-x^4y^4=\left(x^2y^2-1\right)^2+\frac{1}{2}\left(x^4y^4-1\right)^2-\frac{5}{2}\ge-\frac{5}{2}.\)

Dấu = xảy ra khi x=y=1

cho M=\(\frac{x^2}{\left(x+y\right)\left(1-y\right)}-\frac{y^2}{\left(x+y\right)\left(1+x\right)}-\frac{x^2y^2}{\left(1+x\right)\left(1-y\right)}\)

a ) Rút Gọn M

b ) Tìm x,y\(\in\)Z để M=-7

Rút gọn biểu thức

\(\left(\frac{1}{x^2}+\frac{1}{y^2}+\frac{2}{x+y}\left(\frac{1}{x}+\frac{1}{y}\right)\right):\frac{x^3+y^3}{x^2y^2}\)