Thực hiện các phép tính :

a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)

b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)

c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)

d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)

e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)

Làm tính trừ phân thức :

a) \(\dfrac{3x-2}{2xy}-\dfrac{7x-4}{2xy}\)

b) \(\dfrac{3x+5}{4x^3y}-\dfrac{5-15x}{4x^3y}\)

c) \(\dfrac{4x+7}{2x+2}-\dfrac{3x+6}{2x+2}\)

d) \(\dfrac{9x+5}{2\left(x-1\right)\left(x+3\right)^2}-\dfrac{5x-7}{2\left(x-1\right)\left(x+3\right)^2}\)

e) \(\dfrac{xy}{x^2-y^2}-\dfrac{x^2}{y^2-x^2}\)

f) \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\)

g)\(\dfrac{x}{5x+5}-\dfrac{x}{10x-10}\)

h) \(\dfrac{x+9}{x^2-9}-\dfrac{3}{x^2+3x}\)

Thực hiện phép tính:

a) \(\dfrac{x+2y}{xy}\div\dfrac{x^2+4xy+4y^2}{2x^2}\)

b) \(\dfrac{4x^3-xy^2}{x^2+xy+y^2}\div\dfrac{\left(2x-y\right)^3}{x^3-y^3}\)

c) \(\dfrac{x+3}{x+2}\div\dfrac{3x+9}{2x-1}\div\dfrac{4x-2}{2x+4}\)

d) \(\dfrac{x+1}{x+2}\div\left(\dfrac{2x^2}{2x-3}\times\dfrac{3x+3}{4x^3}\right)\)

1) Cho P = \(\left(\dfrac{4x-x^3}{1-4x^2}-x\right):\left(\dfrac{4x^2-x^4}{1-x^2}+1\right)\)

a) rút gọn b) tìm x để P > 0

2) Cho Q = \(\left(\dfrac{x}{x^2-3x+9}-\dfrac{11}{x^3+27}+\dfrac{1}{x+3}\right):\dfrac{x^2-1}{x+3}\)

a) rút gọn b) tìm GTLN

3) Cho A = \(\dfrac{1}{\left(x-y\right)^3}\left(\dfrac{1}{x^3}-\dfrac{1}{y^3}\right)+\dfrac{3}{\left(x-y\right)^4}\left(\dfrac{1}{x^2}+\dfrac{1}{y^2}\right)+\dfrac{6}{\left(x-y\right)^5}\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\)

chứng minh A là lập phương một số hữu tỉ

Giải hệ phương trình:

a)\(\left\{{}\begin{matrix}\dfrac{3x+2}{x-1}-\dfrac{3y-1}{y+2}=0\\\dfrac{2}{x-1}+\dfrac{3}{y+2}=1\end{matrix}\right.\)

b)\(\left\{{}\begin{matrix}\dfrac{4x-5}{x+1}+\dfrac{2y-3}{y-5}=8\\\dfrac{3}{x+1}-\dfrac{2}{y-5}=-1\end{matrix}\right.\)

c)\(\left\{{}\begin{matrix}\dfrac{x+y-2}{x+1}+\dfrac{3-x}{y+1}=\dfrac{5}{4}\\\dfrac{3\left(x+y-2\right)}{x+1}-\dfrac{5-x+2y}{y+1}=\dfrac{3}{4}\end{matrix}\right.\)

d)\(\left\{{}\begin{matrix}\dfrac{x-y+1}{x-3}+\dfrac{x+1}{y-3}=\dfrac{-7}{2}\\\dfrac{2\left(x-y+1\right)}{x-3}-\dfrac{x+y-2}{y-3}=-\dfrac{9}{2}\end{matrix}\right.\)

e)\(\left\{{}\begin{matrix}x^2-y^2+2y=1\\\left(x+y\right)^2-2x-2y=0\end{matrix}\right.\)

f)\(\left\{{}\begin{matrix}4x^2+y^2-4xy=4\\x^2+y^2-2\left(xy+8\right)=0\end{matrix}\right.\)

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. \(\left(\dfrac{1+x}{1-x}-\dfrac{1-x}{1+x}\right)\left(\dfrac{3}{4x}+\dfrac{x}{4}-x\right)\)