Violympic toán 8

giải pt

1,\(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)

2,\(\frac{x+4}{2x^2-5x+2}+\frac{x+1}{2x^2-7x+3}=\frac{2x+5}{2x^2-7x+3}\)

3,\(\frac{x+1}{x-1}-\frac{x-1}{x+1}=3x\left(1-\frac{x-1}{x+1}\right)\)

4,\(\frac{2x}{x-1}+\frac{4}{x^2+2x-3=}=\frac{2x-5}{x+3}\)

5,\(\frac{1}{x-1}-\frac{7}{x+2}=\frac{3}{x^2+x-2}\)

6,\(\frac{x+3}{x-4}+\frac{x-1}{x-2}=\frac{2}{6x-8-x^2}\)

7,\(\frac{1}{x-1}-\frac{7}{x+2}=\frac{3}{1-x^2}\)

\(\frac{2}{x+2}-\frac{2x^2+16}{x^3+8}=\frac{5}{x^2-2x+4}\)

\(\frac{2}{x^2-4}-\frac{x-1}{x\left(x-2\right)}+\frac{\left(x-4\right)}{x\left(x+2\right)}=0\)

\(\frac{1}{x-2}\frac{6}{x+3}=\frac{5}{6-x^2-x}\)

\(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^2-x+1}=\frac{2\left(x+2\right)^2}{x^6-1}\)

Bài 1: Giải các phương trình:

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

b) \(x+\frac{1}{x}=2\)

Bài 2: Giải các phương trình:

a) \(\frac{x}{x-2}=\frac{x-2}{x-3}\)

b) \(\frac{2x-4}{x-1}-\frac{x-3}{x-2}=1\)

c) \(\frac{x+3}{x-1}-\frac{3}{X-1}+\frac{x^2-2}{1-x^2}=0\)

d) \(\frac{2x+1}{x-3}-\frac{3}{x-2}=2\)

Bài 3: Giải các phương trình sau:

a) \(\frac{2x}{x-1}-\frac{x}{x-2}=\frac{x^2}{\left(x-1\right)\left(x-2\right)}\)

b) \(\frac{1}{x+2}\frac{6}{x-1}+\frac{8}{\left(x+2\right)\left(x-1\right)}=0\)

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

d) \(\frac{x-1}{x+2}-\frac{x+1}{x-2}=\frac{x-3}{4-x^2}\)

a, (x-1)³ - x(x-1)² = 5(2-x) - 11(x+2)

b, (x-2)³ + (3x-1)(3x+1) = (x+1)³

c, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{5}\)

d, \(\frac{2\left(x-3\right)}{7}+\frac{x-5}{3}=\frac{13x+4}{21}\)

e, \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)

3) \(\frac{1-x}{x+1}-\frac{3+2x}{x+1}=0\)

13) \(\frac{x+2}{x}-\frac{x^2+5x+4}{x\left(x+2\right)}=\frac{x}{x+2}\)

14) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{20}{\left(x+1\right)\left(2-x\right)}\)

16) \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)

17) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)

18) \(\frac{x-1}{x}+\frac{1}{x+1}=\frac{2x-1}{2x^2+2}\)

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

20) \(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}\)