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Ta có: \(\frac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}\)
\(=\frac{x^2y+xy^2+xy^2+y^3}{2x^2+2xy-xy-y^2}\)
\(=\frac{xy\left(x+y\right)+y^2\left(x+y\right)}{2x\left(x+y\right)-y\left(x+y\right)}\)
\(=\frac{\left(x+y\right)\left(xy+y^2\right)}{\left(2x-y\right)\left(x+y\right)}=\frac{xy+y^2}{2x-y}\left(đpcm\right)\)
Ta có: \(\frac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}\)
\(=\frac{x^2+xy+2xy+2y^2}{x^2\left(x+2y\right)-y^2\left(x+2y\right)}\)
\(=\frac{x\left(x+y\right)+2y\left(x+y\right)}{\left(x^2-y^2\right)\left(x+2y\right)}\)
\(=\frac{\left(x+2y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)\left(x+2y\right)}=\frac{1}{x-y}\left(đpcm\right)\)
\(\frac{x^2+xy-y^2}{2x^2-3xy+y^2}\)
\(=\frac{x^1+xy-y^1}{2x^1-3xy+y^1}\)
Vậy: Phân thức có thể rút gọn cho 2
P/s: Ko chắc đâu nhé :v
a) (2x^2 +2xy - xy -y^2 ) / (2x^2 - 2xy - xy +y^2)
= 2x(x+y) - y(x+y) / 2x(x-y) - y(x-y)
= (2x-y)(x+y) / (2x-y)(x-y)
= x+y/x-y
Rút gọn cái sau:
\(\frac{32x+4x^2+2x^3}{x^3+64}\)
\(=\frac{2x\left(x^2+2x+16\right)}{\left(x+4\right)\left(x^2-4x+16\right)}\)
Đề có vẻ sai sai ?
c) hang dang thuc ( x -y+z)^2
o duoi phan h hang dang thuc luon
a) phan h nhan tu ra sao cho co tử la (x-1)(3x^2 -4x +1)
mau la (x-1)(2x^2 -x-3)
b ) k nhin dc de
b: \(=\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}\)
\(=\dfrac{\left(x+2\right)\left(x+3\right)+\left(x+1\right)\left(x+3\right)+\left(x+2\right)\left(x+1\right)}{\left(x+2\right)^2\cdot\left(x+1\right)\left(x+3\right)}\)
\(=\dfrac{x^2+5x+6+x^2+4x+3+x^2+3x+2}{\left(x+2\right)^2\cdot\left(x+1\right)\left(x+3\right)}\)
\(=\dfrac{3x^2+12x+11}{\left(x+2\right)^2\cdot\left(x+1\right)\left(x+3\right)}\)