\(\frac{2x-1}{MTC}+\frac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{MTC}-\frac{\left(\sqrt{2x}+\sqrt{x}\left(\sqrt{2x}+1\right)\right)}{MTC}\)

=\(\frac{2x-1+x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1-2x-\sqrt{2x}-x\sqrt{2}-\sqrt{x}}{MTC}\)

=\(\frac{-2\sqrt{x}-2}{\left(\sqrt{2x}-1\right)\left(\sqrt{2x+1}\right)}\)

Tính

\(A=\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10-5}\)

\(B=\left(\frac{1}{x^2+x}-\frac{2-x}{x+1}\right):\left(\frac{1}{x}+x-2\right)\)

\(C=\frac{1}{x-1}-\frac{x^3-x}{x^2+1}\left(\frac{1}{x^2-2x+1}+\frac{1}{1-x^2}\right)\)

\(1.\frac{1}{x^2-2x+2}+\frac{2}{x^2-2x+3}=\frac{6}{x^2-2x+4} \)
2.\(\frac{2x^4}{\left(x+1\right)^2}-\frac{5x^2}{x+1}+2=0\)
3.\(\left(x+\frac{1}{x}\right)^2-6\left(x+\frac{1}{x}\right)+8=0\)
4.\(\left(x^2+\frac{1}{x^2}\right)-4\left(x+\frac{1}{x}\right)+6=0\)
5.\(\frac{2x}{3x^2-x+2}-\frac{7x}{3x^2+5x+2}=1\)

1. \(\frac{x-1}{2x-3}=\frac{-3x+1}{\left|x+1\right|}\)

2. \(\frac{x^2-\left|x\right|-12}{x-3}=2x\)

3. \(\frac{2x-3}{\left|x+2\right|}=\frac{3}{x-1}\)

4. \(\frac{x+2}{2x-1}=\frac{-x+3}{\left|2x+1\right|}\)

cm các biểu thức sau ko phụ thuộc vào biến:

a,\(\left[\frac{2\left(x+1\right)\left(y+1\right)}{\left(x+1\right)^2-\left(y+1\right)^2}+\frac{x-y}{2x+2y+4}\right].\frac{2x+2}{x+y+2}+\frac{y+1}{y-x}\)

b,\(\left[2\left(x+y\right)+1-\frac{1}{1-2x-2y}\right]:\left[2x+2y-\frac{4x^2+8xy+4y^2}{2x+2y-1}\right]+2\left(x+y\right)\)

CMR:
\(\left(\frac{X^2-2X}{2X^2-8}-\frac{2X^2}{8-4X+2X^2-3X^3}\right).\left(1-\frac{1}{X}-\frac{2}{X^2}\right)=\frac{X+1}{2X}\)

Tính

\(A=\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10-5}\)

\(B=\left(\frac{1}{x^2+x}-\frac{2-x}{x+1}\right):\left(\frac{1}{x}+x-2\right)\)