cho biểu thức
P=\(\left(\dfrac{1}{2x-y}+\dfrac{3y}{y^2-4x^2}-\dfrac{2}{2x+y}\right):\left(\dfrac{4x^2+y^2+1}{4x^2-y^2}\right)\)
a) rút gọn P
b) tìm x để P=\(\dfrac{1}{2}\)
Tìm tập xác định của biểu thức, rút gọn biểu thức, rồi tính giá trị của biểu thức với x = \(\dfrac{1}{3}\) , y = -2:
[\(\dfrac{2x}{2x-3y}\) - \(\dfrac{9y^2\left(3y+4x\right)}{8x^3-37y^3}\) - \(\dfrac{24xy}{4x^2+6xy+9y^2}\)][2x + \(\dfrac{3y\left(3y+4x\right)}{2x-3y}\)]
Đặt bthuc = A nhé
ĐKXĐ : \(2x\ne3y\)
\(A=\left[\dfrac{2x\left(4x^2+6xy+9y^2\right)}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}-\dfrac{27y^3+36xy^2}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}-\dfrac{24xy\left(2x-3y\right)}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\right]\left[\dfrac{2x\left(2x-3y\right)}{\left(2x-3y\right)}+\dfrac{9y^2+12xy}{\left(2x-3y\right)}\right]\)\(=\left[\dfrac{8x^3+12x^2y+18xy^2-27y^3-36xy^2-48x^2y+72xy^2}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\right]\left[\dfrac{4x^2-6xy+9y^2+12xy}{\left(2x-3y\right)}\right]\)
\(=\dfrac{8x^3-36x^2y+36xy^2-27y^3}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\cdot\dfrac{4x^2+6xy+9y^2}{2x-3y}\)
\(=\dfrac{\left(2x-3y\right)^3}{\left(2x-3y\right)^2}=2x-3y\)
Với x = 1/3 ; y = -2 (tmđk) thay vào A ta được : A = 2.1/3 - 3.(-2) = 20/3
Rút gọn các biểu thức:
a) {\(\dfrac{1}{x^2}\) + \(\dfrac{1}{y^2}\) + \(\dfrac{2}{x+y}\)(\(\dfrac{1}{x}\) + \(\dfrac{1}{y}\))} : \(\dfrac{x^3+y^3}{x^2y^2}\)
b) {\(\dfrac{1}{\left(2x-y\right)^2}\) + \(\dfrac{2}{4x^2-y^2}\) + \(\dfrac{1}{\left(2x+y\right)^2}\)} . \(\dfrac{4x^2+4xy+y^2}{16x}\)
c) (\(\dfrac{x^2-xy}{x^2y+y^3}\) - \(\dfrac{2x^2}{y^3-xy^2+x^2y-x^3}\))(1 - \(\dfrac{y-1}{x}\) - \(\dfrac{y}{x^2}\))
Rút gọn các biểu thức sau :
a)\(\dfrac{25xy^3\left(2x-y\right)^2}{75xy^2\left(y-2x\right)}\)
b)\(\dfrac{x^2-y^2}{x^2-y^2+xz-yz}\)
c)\(\dfrac{\left(2x+3\right)-x^2}{x^2-1}\)
d)\(\dfrac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
`a,(25xy^3(2x-y)^2)/(75xy^2(y-2x))(x,y ne 0)(y ne 2x)`
`=(25xy^3(y-2x)^2)/(75xy^2(y-2x))`
`=(y(y-2x))/3`
`b,(x^2-y^2)/(x^2-y^2+xz-yz)`
`=((x-y)(x+y))/((x-y)(x+y)+z(x-y))`
`=(x+y)/(x+y+z)`
`c,((2x+3)-x^2)/(x^2-1)(x ne +-1)`
`=(-(x^2-3x+x-3))/((x-1)(x+1))`
`=(-x(x-3)+x-3)/((x-1)(x+1))`
`=((x-3)(1-x))/((x-1)(x+1))`
`=(3-x)/(1+x)`
`d,(3x^3-7x^2+5x-1)/(2x^3-x^2-4x+3)`
`=(3x^3-3x^2-4x^2+4x+x-1)/(2x^3-2x^2+x^2-x-3x+3)`
`=(3x^2(x-1)-4x(x-1)+x-1)/(2x^2(x-1)+x(x-1)-3(x-1))`
`=(3x^2-4x+1)/(2x^2+x-3)`
`=(3x^2-3x-x+1)/(2x^2-2x+3x-3)`
`=(3x(x-1)-(x-1))/(2x(x-1)+3(x-1))`
`=(3x-1)/(2x+3)`
a) Ta có: \(\dfrac{25xy^3\cdot\left(2x-y\right)^2}{75xy^2\cdot\left(y-2x\right)}\)
\(=\dfrac{25xy^2\cdot y\cdot\left(y-2x\right)^2}{25xy\cdot y\cdot\left(y-2x\right)\cdot3}\)
\(=\dfrac{y\left(y-2x\right)}{3}\)
cho biểu thức
P =\(\left(\dfrac{1}{2x-y}+\dfrac{3y}{y^2-4x^2}-\dfrac{2}{2x+y}\right)\)
a) rút gọn P
b) tìm x để P=\(\dfrac{1}{2}\)
a) P = (\(\dfrac{1}{2x-y}\) + \(\dfrac{3y}{y^2-4x^2}\) - \(\dfrac{2}{2x+y}\) )
= (\(\dfrac{1}{2x-y}\) - \(\dfrac{3y}{4x^2-y^2}\) - \(\dfrac{2}{2x+y}\) )
= ( \(\dfrac{2x+y}{\left(2x-y\right)\left(2x+y\right)}\) - \(\dfrac{3y}{\left(2x+y\right)\left(2x-y\right)}\) - \(\dfrac{2\left(2x-y\right)}{\left(2x-y\right)\left(2x+y\right)}\) )
= \(\dfrac{2x+y-3y-4x+2y}{\left(2x-y\right)\left(2x+y\right)}\) = \(\dfrac{-2x}{\left(2x+y\right)\left(2x-y\right)}\)
Rút gọn, rồi tính giá trị các phân thức sau : A=\(\dfrac{\left(2x^{2^{ }}+2x^{ }\right)\left(x-2\right)^2}{^{ }\left(x^{3^{ }}-4x\right)\left(x+1\right)}\)với x = \(\dfrac{1}{2}\)
B=\(\dfrac{x^3-x^{2^{ }}y+xy^2}{x^3+y^3}\)với x = -5 , y = 10
\(A=\dfrac{2x\left(x+1\right)\left(x-2\right)^2}{x\left(x-2\right)\left(x+2\right)\left(x+1\right)}=\dfrac{2\left(x-2\right)}{x+2}\\ A=\dfrac{2\left(\dfrac{1}{2}-2\right)}{\dfrac{1}{2}+2}=\dfrac{2\left(-\dfrac{3}{2}\right)}{\dfrac{5}{2}}=\left(-3\right)\cdot\dfrac{2}{5}=-\dfrac{6}{5}\)
\(B=\dfrac{x\left(x^2-xy+y^2\right)}{\left(x+y\right)\left(x^2-xy+y^2\right)}=\dfrac{x}{x+y}=\dfrac{-5}{-5+10}=\dfrac{-5}{5}=-1\)
Thực hiện phép tính , rút gọn bt
\(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
\(\dfrac{x+y}{2\left(x-y\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
A= \(\left(\dfrac{x+y}{y}-\dfrac{2y}{y-x}\right):\left(\dfrac{x^2+y^2}{y-x}\right)+\left(\dfrac{x^2+1}{2x-1}-\dfrac{x}{2}\right).\dfrac{1-2x}{x+2}\)
Với điều kiện của x, y để A có nghĩa, hãy rút gọn biểu thức trên
\(A=\dfrac{x^2-y^2+2y^2}{y\left(x-y\right)}\cdot\dfrac{-\left(x-y\right)}{x^2+y^2}+\dfrac{2x^2+2-2x^2+x}{2\left(2x-1\right)}\cdot\dfrac{-\left(2x-1\right)}{x+2}\)
\(=\dfrac{-1}{y}+\dfrac{-1}{2}=\dfrac{-2-y}{2y}\)
Thực hiện các phép tính sau :
a) \(\left(\dfrac{5x+y}{x^2-5xy}+\dfrac{5x-y}{x^2+5xy}\right).\dfrac{x^2-25y^2}{x^2+y^2}\)
b) \(\dfrac{4xy}{y^2-x^2}:\left(\dfrac{1}{x^2+2xy+y^2}-\dfrac{1}{x^2-y^2}\right)\)
c) \(\left[\dfrac{1}{\left(2x-y\right)^2}+\dfrac{2}{4x^2-y^2}+\dfrac{1}{\left(2x+y\right)^2}\right].\dfrac{4x^2+4xy+y^2}{16x}\)
d) \(\left(\dfrac{2}{x+2}-\dfrac{4}{x^2+4x+4}\right):\left(\dfrac{2}{x^2-4}+\dfrac{1}{2-x}\right)\)
Rút gọn biểu thức:
\(\left(\dfrac{y}{xy-2x^2}-\dfrac{2}{y^2+y-2xy-2x}\right)\left(1+\dfrac{3y+y^2}{3+y}\right)\)