thực hiện phép tính \(\frac{x^2-y^2}{6x^2y^2}\div\frac{x+y}{3xy}\)
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Thực hiện phép tính
\(\frac{3xy^2+x^2y}{xy\left(x-y\right)}\)- \(\frac{3x^2y+xy^2}{xy\left(x-y\right)}\)
\(ĐKXĐ:x\ne y,x\ne0,y\ne0\)
Ta có : \(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}=\frac{-2xy.\left(x-y\right)}{xy.\left(x-y\right)}=-2\)
\(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y}{xy\left(x-y\right)}+\frac{-\left(3x^2y+xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{\left(3xy^2-3x^2y\right)+\left(x^2y-xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy.\left(y-x\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{\left(x-y\right).\left(-3xy+xy\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy+xy}{xy}\)
\(=\frac{-2xy}{xy}\)
\(=-2.\)
\(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy\left(x-y\right)}\)( ĐKXĐ : \(x\ne y;x,y\ne0\))
= \(\frac{3xy^2+x^2y-3x^2y-xy^2}{xy\left(x-y\right)}\)
\(=\frac{xy^2\left(3-1\right)+x^2y\left(1-3\right)}{xy\left(x-y\right)}\)
\(=\frac{xy^2\left(3-1\right)-x^2y\left(3-1\right)}{xy\left(x-y\right)}\)
\(=\frac{2\left(xy^2-x^2y\right)}{xy\left(x-y\right)}\)
\(=\frac{2xy\left(y-x\right)}{-xy\left(y-x\right)}\)
\(=-2\)
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Thực hiện phép tính :
a) \(\dfrac{3x+2}{x^2}\div\dfrac{6x+4}{2x^2}\)
b) \(\dfrac{4xy}{x+y}\div\dfrac{6x^2y^3}{x^2-y^2}\)
`a)[3x+2]/[x^2]:[6x+4]/[2x^2]`
`=[3x+2]/[x^2].[2x^2]/[2(3x+2)]`
`=1`
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`b)[4xy]/[x+y]:[6x^2y^3]/[x^2-y]`
`=[4xy]/[x+y].[(x-y)(x+y)]/[6xy.xy^2]`
`=[2(x-y)]/[3xy^2]=[2x-2y]/[3xy^2]`
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thực hiện phép tính
\(\sqrt{50x^3y^5}-\frac{2y^2}{x^2}\sqrt{32x^7y}+\frac{3xy}{2}\sqrt{2xy^3},x>0,y>0\)
thực hiện phép tính
\(\sqrt{50^3y^5}-\frac{2y^2}{x^2}\sqrt{32x^7y}+\frac{3xy}{2}\sqrt{2xy^3},x>0,y>0\)
Kết quả rất lẻ : \(\frac{-16y^2\sqrt{x^7y}+3x^3y\sqrt{xy^3}+500x^2\sqrt{y^5}}{\sqrt{2}x^2}\)
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1, Thực hiện tính cộng, trừ, nhân, chia các phân thức sau:
a,\(\frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\)
b,\(\frac{2x+3}{4x^2y^2}:\frac{6x+9}{10x^2y}\)
c,\(\frac{x^2-y^2}{6x^2y^2}:\frac{x+y}{3xy}\)
d,\(\left(\frac{3x}{1-3x}+\frac{2x}{3x+1}\right):\frac{6x^2+10x}{1-6x+9x^2}\)
a) \(\frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\)
\(=\frac{2x-7}{10x-4}-\frac{-\left(3x+5\right)}{-\left(4-10x\right)}\)
\(=\frac{2x-7}{10x-4}-\frac{5-3x}{10x-4}\)
\(=\frac{2x-7-\left(5-3x\right)}{10x-4}\)
\(=\frac{2x-7-5+3x}{10x-4}\)
\(=\frac{5x-12}{10x-4}\)
8,Thực hiện phép tínha,frac{5x^2-y^2}{xy}-frac{3x-2y}{y}b,frac{3}{2x+6}-frac{x-6}{2x^2+6x}c,frac{2x}{x^2+2xy}+frac{y}{xy-2y^2}+frac{4}{x^2-4y^2} d,frac{1}{x-y}+frac{3xy}{y^3-x^3}+frac{x-y}{x^2+xy+y^2} e,frac{2x+y}{2x^2-xy}+frac{16x}{y^2-4x^2}+frac{2x-y}{2x^2+xy} f,frac{1}{1-x}+frac{1}{1+x}+frac{2}{1+x^2}+frac{4}{1+x^4}+frac{8}{1+x^8}+frac{16}{1+x^{16}}
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8,Thực hiện phép tính
a,\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)
b,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
c,\(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)
d,\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
e,\(\frac{2x+y}{2x^2-xy}+\frac{16x}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
f,\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
Thực hiện phép tính
\(\left(x^2y-\frac{1}{2}xy+y^2\right).\left(x-\frac{1}{2}y\right)-x^2y\left(x-\frac{1}{2}\right)\)
Bài 1: Tính:
a) x^2-9/2x+6 : 3-x/2
b) 2x/x-y - 2y/x-y
c) x+15/x^2-9 + 2/x+3
d)x+y/2x+2y - x-y/2x+2y - y^2+x^2/y^2-x^2
Bài 2: Rút gọn:
a) x^3-x/3x+3
b) x^2+3xy/x^2-9y^2
Bài 3: Thực hiện phép tính:
a) x/x-3 + 9-6x/x^2-3x
b) 6x-3/x : 4x^2-1/3x^2
thực hiện phép cộng
\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
\(=\frac{1}{x+y}-\frac{3xy}{x^3-y^3}+\frac{x-y}{x^2+xy+y^2}\)
\(=\frac{1.\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\frac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\frac{\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{2x^2-4xy+2y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\frac{2\left(x^2-2xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\frac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\frac{2\left(x-y\right)}{x^2+xy+y^2}\)
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