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24 tháng 5 2017
a)\(\frac{x^2+y^2-1+2xy}{x^2-y^2+1+2x}\)
\(\Leftrightarrow\frac{\left(x+y\right)^2-1}{\left(x+1\right)^2-y^2}\)
\(\Leftrightarrow\frac{\left(x+y+1\right)\left(x+y-1\right)}{\left(x+1-y\right)\left(x+1+y\right)}\)
\(\Leftrightarrow\frac{x+y-1}{x-y+1}\)
b)\(\frac{3x^3-6x^2y+xy^2-2y^3}{9x^5-18x^4y-xy^4+2y^5}\)
\(\Leftrightarrow\frac{3x^2\left(x-2y\right)+y^2\left(x-2y\right)}{9x^4\left(x-2y\right)-y^4\left(x-2y\right)}\)
\(\Leftrightarrow\frac{\left(3x^2+y^2\right)\left(x-2y\right)}{\left(9x^4-y^4\right)\left(x-2y\right)}\)
\(\Leftrightarrow\frac{3x^2+y^2}{\left(3x^2-y^2\right)\left(3x^2+y^2\right)}\)
\(\Leftrightarrow\frac{1}{3x^2-y^2}\)
SH
1
D
4 tháng 11 2018
\(\frac{2xy}{x^2-y^2}+\frac{x-y}{2x+2y}\)
\(=\frac{2xy}{\left(x-y\right)\left(x+y\right)}+\frac{x-y}{2\left(x+y\right)}\)
\(=\frac{4xy}{2\left(x-y\right)\left(x+y\right)}+\frac{\left(x-y\right)\left(x-y\right)}{2\left(x+y\right)\left(x-y\right)}\)
\(=\frac{4xy+x^2-xy-xy-y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\frac{2xy+x^2-y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\frac{\left(x-y\right)^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\frac{x-y}{2\left(x+y\right)}=\frac{x-y}{2x+2y}\)
KN
29 tháng 11 2019
Ta có: \(\frac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}\)
\(=\frac{x^2y+xy^2+xy^2+y^3}{2x^2+2xy-xy-y^2}\)
\(=\frac{xy\left(x+y\right)+y^2\left(x+y\right)}{2x\left(x+y\right)-y\left(x+y\right)}\)
\(=\frac{\left(x+y\right)\left(xy+y^2\right)}{\left(2x-y\right)\left(x+y\right)}=\frac{xy+y^2}{2x-y}\left(đpcm\right)\)
KN
29 tháng 11 2019
Ta có: \(\frac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}\)
\(=\frac{x^2+xy+2xy+2y^2}{x^2\left(x+2y\right)-y^2\left(x+2y\right)}\)
\(=\frac{x\left(x+y\right)+2y\left(x+y\right)}{\left(x^2-y^2\right)\left(x+2y\right)}\)
\(=\frac{\left(x+2y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)\left(x+2y\right)}=\frac{1}{x-y}\left(đpcm\right)\)
TN
1
7 tháng 7 2016
Rút gọn :
a ) \(\frac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}\)
\(=\frac{y\left(x^2+2xy+y^2\right)}{2x^2+2xy-xy-y^2}\)
\(=\frac{y\left(x+y\right)^2}{2x\left(x+y\right)-y\left(x+y\right)}\)
\(=\frac{y\left(x+y\right)}{2x-y}\)
\(=\frac{xy+y^2}{2x-y}\)
H
15 tháng 12 2018
\(\frac{x}{x-2y}+\frac{x}{x+2y}+\frac{4xy}{4y^2-x^2}\)
\(=\frac{x\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\frac{x\left(x-2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\frac{-4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{x^2+2xy+x^2-2xy-4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{2x^2-4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(\frac{2x^2y+2xy+2y}{x^5+x+1}=\frac{2y\left(x^2+x+1\right)}{x^3.x^2+x+1}=\frac{2y}{x^3}\)
#Học tốt!!!
\(\frac{2x^2y+2xy+2y}{x^5+x+1}=\frac{2y\left(x^2+x+1\right)}{x^5-x^2+x^2+x+1}.\)
\(=\frac{2y\left(x^2+x+1\right)}{x^2\left(x^3-1\right)+x^2+x+1}\)
\(=\frac{2y\left(x^2+x+1\right)}{x^2\left(x-1\right)\left(x^2+x+1\right)+x^2+x+1}\)
\(=\frac{2y\left(x^2+x+1\right)}{\left(x^2+x+1\right)\left[x^2\left(x-1\right)+1\right]}\)
\(=\frac{2y}{x^3-x^2+1}\)