Tìm x : \(\frac{2\left(x-1\right)\left(x-3\right)}{3}-\frac{4\left(2x-1\right)^2}{5}=\frac{\left(1+3x\right)^2}{2}-3x\left(1-x\right)\)
Giải các phương trình:
a) \(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\)
b) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\frac{1}{x+2}=\frac{12}{8+x^3}\)
d) \(\frac{13}{\left(x-3\right)\left(2x+7\right)}+\frac{1}{2x+7}=\frac{6}{\left(x-3\right)\left(x+3\right)}\)
Rút gọn A : \(\left[\frac{\left(x-1\right)^2}{3x+\left(x-1\right)^2}-\frac{1-2x^2+4x}{x^3-1}+\frac{1}{x-1}\right]:\frac{2x}{x^3+x}\)
Rút gọn A = \(\left[\left(1+\frac{1}{x^2}\right)\div\left(1+2x+x^2\right)+\frac{2}{\left(x+1\right)^3}\left(1+\frac{1}{x}\right)\right]\div\frac{x-1}{x^3}\)
Tìm tập xác định
Tìm x: \(\left(3x-1\right)^3-2\left(2x-3\right)^2-3\left(x-2\right)\left(3-x\right)=\left(1+3x\right)^3-2\left(1+3x\right)^2\)
Tìm tập xác định
Rút gọn : \(\left[\left(x^3-1-\frac{7-x^3}{3+x^3}\right).\frac{4}{x^5+3x^2}\right]:\left[\frac{3x^6-12}{x^9+6x^6+9x^3}.\frac{x}{3x^3+6}\right]\)
1)\(\frac{8xy\left(3x-1\right)^3}{12x^3\left(1-3x\right)}\)
2)\(\frac{5x^3+5x}{x^4-1}\)
3)\(\frac{9-\left(x+5\right)^2}{x^2+4x+4}\)
4)\(\frac{32x-8x^2+2x^3}{x^3+64}\)
Tìm x: \(\left(2x-1\right)^3-3\left(3x+1\right)^2=\left(3+2x\right)^3-2\left(2-x\right)^2-\left(x-1\right)\left(x+2\right)\)