\(\dfrac{2xy}{\dfrac{x^3}{y}}=2xy.\dfrac{y}{x^3}=\dfrac{2xy^2}{x^3}=\dfrac{2y^2}{x^2}\)
\(\dfrac{2xy}{\dfrac{x^3}{y}}=2xy.\dfrac{y}{x^3}=\dfrac{2xy^2}{x^3}=\dfrac{2y^2}{x^2}\)
thực hiện phép cộng
\(\dfrac{3}{x^2+2xy+y^2}\)+ \(\dfrac{4}{2xy-x^2-y^2}\)+\(\dfrac{5}{x^2-y^2}\)
giúp mình với
Tính :
a)\(\dfrac{6x-3}{5x^2+x}.\dfrac{25x^2+10x+1}{1-8x^3}\)
b)\(\dfrac{3x^2-x}{x^2-1}.\dfrac{1-x^4}{\left(1-3x\right)^3}\)
c)\(\dfrac{x^4-xy^3}{2xy+y^2}:\dfrac{x^3+x^2y+xy^2}{2x+y}\)
d) \(\dfrac{5x^2-10xy+5y^2}{2x^2-2xy+2y^2}:\dfrac{8x-8y}{x^3+10y^3}\)
Tinh:
\(\dfrac{2xy}{x^2-y^2}+\dfrac{x-y}{2x+2y}+\dfrac{y}{y-x}\)
Thực hiện phép tính:
1. \(\dfrac{x^2}{x+1}+\dfrac{2x}{x^2-1}-\dfrac{1}{1-x}+1\)
2. \(\dfrac{1}{x^3-x}-\dfrac{1}{\left(x-1\right)x}+\dfrac{2}{x^2-1}\)
3. \(\dfrac{y}{xy-5y^2}-\dfrac{15y-25x}{y^2-25x^2}\)
4. \(\dfrac{4-2x+x^2}{2+x}-2-x\)
5. \(\dfrac{2x^3-2y^3}{3x+3y}:\dfrac{2x^2+2xy+y^2}{x^2+2xy+y^2}\)
6. \(\left(\dfrac{1+x}{1-x}-\dfrac{1-x}{1+x}\right)\left(\dfrac{3}{4x}+\dfrac{x}{4}-x\right)\)
e)\(\dfrac{2xy-x^2+z^2-y^2}{x^2+2-y^2+2xz}=\)
g)\(\dfrac{x^3+2x^2-x-z}{x^3-3x+2}=\)
chứng minh rằng: \(\dfrac{2x^2+3xy+y^2}{2x^3+x^2y-2xy^2-y^3}=\dfrac{1}{x-y}\)
Tìm phân thức Q, biết: \(\dfrac{x-y}{x^3+y^3}.Q=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}\)
Giải PTNN:
a)\(x^2+2y^2+z^2-2xy-2y+2z+2=0\)
b)\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{6xy}=\dfrac{1}{6}\)
c)\(x^3-y^3=xy+8\)
Giải phương trình nghiệm nguyên:
a)\(x^2+2y^2+z^2-2xy-2y+2z+2=0\)
b)\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{6xy}=\dfrac{1}{6}\)
c)\(x^3-y^3=xy+8\)