x^30+x^28+x^26+.........+x^4+x^2+1/x^28+x^24+x^20+.........+x^8+x^4+1
c) \(\dfrac{y^4-1}{y^3+y^2+y+1}=\)
d)\(\dfrac{2x^2-9x+7}{-2x^2-x+28}=\)
Giải phương trình:
\(8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)=\left(x+4\right)^2\)
Giải các phương trình sau :
1.\(\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
2.\(\dfrac{12}{1-9x^2}=\dfrac{1-3x}{1+3x}-\dfrac{1+3x}{1-3x}\)
3.\(\dfrac{x+5}{x^2-5x}-\dfrac{x+25}{2x^2-50}=\dfrac{x-5}{2x^2+10x}\)
4.\(\dfrac{6x_{ }+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
5.\(\dfrac{2}{x^2-4}-\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x-4}{x\left(x+2\right)}=0\)
6.\(\dfrac{2}{x+2}-\dfrac{2x^2+16}{x^3+8}=\dfrac{5}{x^2-2x+4}\)
Thực hiện phép tính:
1. \(\dfrac{x}{x+1}-\dfrac{2x}{x-1}+\dfrac{x+3}{x^2-1}\)
2. \(\dfrac{5}{x+1}-\dfrac{10}{x-x^2-1}-\dfrac{15}{x^3+1}\)
3. \(\dfrac{2}{2x+1}-\dfrac{1}{2x-1}-\dfrac{2}{1-4x^2}\)
4. \(\dfrac{3x^2+5x+14}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{4}{x+1}\)
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. \(\left(\dfrac{1+x}{1-x}-\dfrac{1-x}{1+x}\right)\left(\dfrac{3}{4x}+\dfrac{x}{4}-x\right)\)
Tính
a)\(\left(\dfrac{\left(x-1\right)^2}{\left(3x+x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right):\dfrac{x^2+x}{x^2+1}\)
b)\(\left(\dfrac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\dfrac{2x^2-x+10}{2\left(x^3+x^2+x+1\right)}\right):\left(\dfrac{5}{x^2+1}+\dfrac{3}{2\left(x+1\right)}-\dfrac{3}{2\left(x-1\right)}\right).\dfrac{2}{x-1}\)
c)\(\left(\dfrac{x^2}{x^2-5x+6}+\dfrac{x^2}{x^2-3x+2}\right):\dfrac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)
a) \(\dfrac{2a-1}{2a+1}-\dfrac{2a-3}{2a-1}\)
b) \(\dfrac{1}{x+1}-\dfrac{1}{x-1}-\dfrac{2x^2}{1-x^2}\)
c) \(\dfrac{x+1}{\left(x+2\right)^2}-\dfrac{1}{x+2}-\dfrac{1}{1-x^2}\)
d) \(\dfrac{x-5}{x^2+3x}+\dfrac{6}{x+3}\)
e) \(x+2+\dfrac{3}{x-2}\)
g) \(\dfrac{4-x}{x^2-4x}+\dfrac{3}{x}+\dfrac{-2}{x+1}\)
h) \(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
i) \(\dfrac{x}{x^2-4x}-\dfrac{3}{5x}\)
k) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
giải các phương trình sau:
a)2x(x-2)+5(x-2)=0
b)\(\dfrac{3x-4}{2}\)-\(\dfrac{4x+1}{3}\)
c)\(\dfrac{2x}{x-1}\)-\(\dfrac{x}{x+1}=1\)