Rút gọn
\(A=\left(\dfrac{x-y}{2y-x}+\dfrac{x^2+y^2+y-2}{2y^2+xy-x^2}\right):\dfrac{4x^2+4x^2y+y^2-4}{x^2+y+xy+x}\)
Rút gọn \(\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}:\dfrac{1}{2x^2+y+2}\)
Cho biểu thức B= (\(\dfrac{x-y}{2y-x}\)-\(\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\)) : \(\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
a) Với giá trị nào của x,y thì BT được xác định
b) Rút gọn BT
a) ĐKXĐ: \(x\ne2y,x\ne-y;x\ne-1\)
b) \(B=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
\(B=\left[\dfrac{y-x}{x-2y}-\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(x-2y\right)}\right]:\dfrac{4x^4+4x^2y+y^2-4}{x\left(x+y\right)+\left(x+y\right)}\)
\(B=\left[\dfrac{\left(y-x\right)\left(x+y\right)}{\left(x-2y\right)\left(x+y\right)}-\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(x-2y\right)}\right]:\dfrac{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}{\left(x+1\right)\left(x+y\right)}\)
\(B=\dfrac{y^2-x^2-x^2-y^2-y+2}{\left(x+y\right)\left(x-2y\right)}:\dfrac{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}{\left(x+1\right)\left(x+y\right)}\)
\(B=\dfrac{-2x^2-y+2}{\left(x+y\right)\left(x-2y\right)}\cdot\dfrac{\left(x+1\right)\left(x+y\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\)
\(B=\dfrac{-\left(2x^2+y-2\right)}{\left(x+y\right)\left(x-2y\right)}\cdot\dfrac{\left(x+1\right)\left(x+y\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\)
\(B=\dfrac{-\left(x+1\right)}{\left(x-2y\right)\left(2x^2+y+2\right)}\)
Rút gọn và tính giá trị của biểu thức sau tại \(x=-1,76;y=\dfrac{3}{25}\)
\(P=\left[\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\right]:\dfrac{x+1}{2x^2+y+2}\)
(Đề thi học sinh giỏi cấp II. Miền Bắc năm 1963)
cho 2 số thực `x,y` thỏa mãn `x>0,y>2,x`\(\ne\)`2y`. CMR: \(\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right)\left(2x^2+y+2\right):\dfrac{x^4+4x^2y^2+y^4-4}{x^2+y+xy+x}=\dfrac{x+1}{2y-x}\)
Đề bài sai, đề đúng thì phân thức đằng sau dấu chia phải là:
\(\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
Rút gọn rồi tính giá trị biểu thức
\(\left[\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+x+xy+y}\right]:\dfrac{x+1}{2x^2+y+2}\)
với x=-1,76 y=\(\dfrac{3}{25}\)
Đặt \(A=\left[\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-1}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+x+xy+y}\right]:\dfrac{x+1}{2x^2+y+2}\)
\(A=\left[\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-1}{\left(x+y\right).\left(x-2y\right)}\right):\dfrac{\left(2x^2+y+2\right).\left(2x^2+y-2\right)}{\left(x+y\right).\left(x+1\right)}\right]:\dfrac{x+1}{2x^2+y+2}\)
\(A=\left(\dfrac{\left(x-y\right).\left(x+y\right)+x^2+y^2+y-2}{\left(x+y\right).\left(2y-x\right)}.\dfrac{\left(x+y\right).\left(x+1\right)}{\left(2x^2+y+2\right).\left(2x^2+y-2\right)}\right):\dfrac{2x^2+y+2}{x+1}\)
\(A=\left(\dfrac{2x^2+y-2}{2y-x}.\dfrac{x+1}{2x^2+y-2}\right).\dfrac{1}{x+1}\)
\(A=\dfrac{1}{2y-x}\)
Thay \(x=-1,76\) và \(y=\dfrac{3}{25}\) vào biểu thức ta được:
\(A=\dfrac{1}{2.\dfrac{3}{25}-\left(-1,76\right)}\)
\(A=\dfrac{1}{2}\)
Rút gọn biểu thức:
\(a,\left(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}\right):\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\)
\(b,\left(\dfrac{x+y}{2x-2y}-\dfrac{x-y}{2x+2y}-\dfrac{2y^2}{y-x}\right):\dfrac{2y}{x-y}\)
Rút gọn biểu thức:
\(a,\left(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}\right):\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\)
\(b,\left(\dfrac{x+y}{2x-2y}-\dfrac{x-y}{2x+2y}-\dfrac{2y^2}{y-x}\right):\dfrac{2y}{x-y}\)
\(a,\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}:\left(\frac{1}{x}+\frac{1}{y}\right)\)
\(=\left(\frac{x}{y\left(x-y\right)}+\frac{y-2x}{x\left(x-y\right)}\right):\left(\frac{y}{xy}+\frac{x}{xy}\right)\)
\(=\left(\frac{x-y}{x\left(x-y\right)}\right):\left(\frac{x+y}{xy}\right)\)
\(=\frac{1}{x}.\frac{xy}{x+y}=\frac{y}{x+y}\)
Rút gọn:
\(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\)
\(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)
\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)
\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)
\(\dfrac{2a\cdot x^2-4ax+2a}{5b-5bx^2}\)
\(=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\)
\(=\dfrac{-2a\left(x-1\right)^2}{5b\left(x-1\right)\left(x+1\right)}=\dfrac{-2a\left(x-1\right)}{5b\left(x+1\right)}\)
\(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)
\(=\dfrac{4x\cdot x-4x\cdot y}{5x^2\cdot x-5x^2\cdot y}\)
\(=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)
\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)
\(=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}\)
=x+y-z
\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3+y^3\right)\left(x^3-y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)
Tìm tập xác định, rồi rút gọn biểu thức:
B = \(\dfrac{y-x}{xy}\) : [\(\dfrac{y^2}{\left(x-y\right)^2\left(x+y\right)}\) - \(\dfrac{2x^2y}{x^4-2x^2y^2+y^4}\) + \(\dfrac{x^2}{\left(y^2-x^2\right)\left(x+y\right)}\)]
Tính giá trị của B với x = -\(\dfrac{1}{2}\), y = 2