\(\dfrac{x^3y+xy^3+xy}{x^3+y^3+x^2y+xy^2+x+y}\)=\(\dfrac{xy\left(x^2+y^2\right)+xy}{\left(x+y\right)\left(x^2-xy+y^2\right)+xy\left(x+y\right)+\left(x+y\right)}\)
=\(\dfrac{xy\left(x^2+y^2+1\right)}{\left(x+y\right)\left(x^2+y^2+1\right)}=\dfrac{xy}{x+y}\)
R/gọn: \(\left(\dfrac{x^2}{x+y}+y\right).\left(\dfrac{1}{x^2-xy}-\dfrac{3y^2}{x^4-xy^3}-\dfrac{y}{x^3+x^2y+xy^2}\right)\)
Rút gọn
\(\dfrac{x^3y+xy^3+xy}{x^3+y^3+x^2y+xy^2+x+y}\)
Rút gọn biểu thức:
\(\dfrac{x^2+xy}{x^2+xy+y^2}\) - [\(\dfrac{x\left(2x^2+xy-y^2\right)}{x^3-y^3}\) - 2 + \(\dfrac{y}{y-x}\)] : \(\dfrac{x-y}{x}\) - \(\dfrac{x}{x-y}\)
Rút gọn các phân thức sau:
a. \(\dfrac{x^3-3x^2-x+3}{x^3-3x}\)
b. \(\dfrac{x^3y+xy^3+xy}{x^3+y^3+x^2y+xy^2+x+y}\)
c. \(\dfrac{\left(3x+2\right)^2-\left(x+2\right)^2}{x^3-x^2}\)
Rút gọn phân thức :
\(\dfrac{x^3+xy^3+xy}{x^3+y^3+x^2y+xy^2+x+y}\)
Help me !!
1 Rút gọn
\(\dfrac{x^3-3x^2+3x-1}{1-x+x^2y-xy}\)
Chứng minh các đẳng thức sau :
a) \(\dfrac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}=\dfrac{xy+y^2}{2x-y}\)
b) \(\dfrac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}=\dfrac{1}{x-y}\)
Rút gọn phân thức
a) \(\dfrac{6x^2y^2}{8xy^5}\)
b) \(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
c) \(\dfrac{2x^2+2x}{x+1}\)
d) \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)
1.Rút gọn :
a,\(\dfrac{xy^3-yx^3}{x^2-xy}\)
b,\(\dfrac{y\left(2x-x^2\right)}{x\left(2y+y^2\right)}\)
