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N
0
HK
2
11 tháng 2 2020
\(\frac{2\left(x+y\right)\left(x-y\right)}{x}-\frac{-2y^2}{x}\)
\(=\frac{2\left(x^2-y^2\right)+2y^2}{x}\)
\(=\frac{2x^2-2y^2+2y^2}{x}\)
\(=\frac{2x^2}{x}\)
\(=2x\)
HL
1
25 tháng 12 2016
DK: \(x\ne0;y\ne0\)
\(\left(\frac{x^2-y^2}{6x^2y^2}\right):\left(\frac{x+y}{3xy}\right)=\left(\frac{\left(x-y\right)\left(x+y\right)}{6x^2y^2}\right).\left(\frac{3xy}{\left(x+y\right)}\right)=\frac{x-y}{2xy}\)
15 tháng 7 2017
a) ĐKXĐ: \(x;y\ne0,x\ne\frac{y}{2},y\ne\frac{x}{2}\)
\(\frac{y}{2x^2-xy}+\frac{4x}{y^2-2xy}=\frac{y}{x\left(2x-y\right)}-\frac{4x}{y\left(2x-y\right)}\)\(=\frac{y^2-4x^2}{xy\left(2x-y\right)}=\frac{\left(y-2x\right)\left(y+2x\right)}{xy\left(2x-y\right)}\)
\(=\frac{-\left(y+2x\right)}{xy}\)
b) ĐKXĐ: \(x\ne2;x\ne-2\)
\(\frac{1}{x+2}+\frac{3}{x^2-4}+\frac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)\(=\frac{1}{x+2}+\frac{3}{\left(x-2\right)\left(x+2\right)}+\frac{x-14}{\left(x+2\right)^2\left(x-2\right)}\)
\(=\frac{\left(x-2\right)\left(x+2\right)+3\left(x+2\right)+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2-4+3x+6+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2+4x-12}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x^2+4x+4\right)-16}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x+2\right)^2-16}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x+2-4\right)\left(x+2+4\right)}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)^2\left(x-2\right)}=\frac{x+6}{\left(x+2\right)^2}\)
30 tháng 10 2018
ĐK: \(x,y\ne0,x\ne\pm y\)
Phép tính trên bằng:
\(\left(\frac{\left(x-y\right)\left(x+y\right)}{xy}-\frac{1}{x+y}.\frac{x^3-y^3}{xy}\right):\frac{x-y}{x}\)
\(=\left(\frac{\left(x-y\right)\left(x+y\right)^2}{xy\left(x+y\right)}-\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(x+y\right)xy}\right):\frac{x-y}{x}\)
\(=\left(\frac{\left(x-y\right)\left(x^2+2xy+y^2-x^2-xy-y^2\right)}{xy\left(x+y\right)}\right):\frac{x-y}{x}\)
\(=\frac{\left(x-y\right)xy}{xy\left(x+y\right)}.\frac{x}{x-y}=\frac{x}{x+y}\)
BA
21 tháng 10 2019
\(a,\left(x+y\right)^2+\left(x-y\right)^2-2\cdot\left(x+y\right)\cdot\left(x-y\right)\)
\(=\left(x+y-x+y\right)^2\)
\(=\left(2y\right)^2=4y^2\)
Hằng đẳng thức thứ 2 nhé
PQ
0
TT
2 tháng 9 2020
\(ĐKXĐ:x\ne y,x\ne0,y\ne0\)
Ta có : \(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}=\frac{-2xy.\left(x-y\right)}{xy.\left(x-y\right)}=-2\)
VM
2 tháng 9 2020
\(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y}{xy\left(x-y\right)}+\frac{-\left(3x^2y+xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{\left(3xy^2-3x^2y\right)+\left(x^2y-xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy.\left(y-x\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{\left(x-y\right).\left(-3xy+xy\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy+xy}{xy}\)
\(=\frac{-2xy}{xy}\)
\(=-2.\)
Ta có: ( x y 2 ) 4 : ( x y 2 ) 2 = x 4 y 8 : x 2 y 4 = x 4 - 2 . y 8 - 4 = x 2 y 4 .