Giải phương trình:

1. \(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)

2. \(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)

3. \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\)

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

5. \(\frac{x-4}{5}-\frac{3x-2}{10}-x=\frac{2x-5}{3}-\frac{7x+2}{6}\)

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

7. \(\frac{\left(x+2\right)^2}{8}-2\left(2x-1\right)=25+\frac{\left(x-2\right)^2}{8}\)

8.\(\frac{7x^2-14x-5}{5}=\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}\)

9. \(\frac{\left(2x-3\right)\left(2x+3\right)}{8}=\frac{\left(x-4\right)^2}{6}+\frac{\left(x-2\right)^2}{3}\)

10. \(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)

Câu 3: Giải các phương trình sau bằng cách đưa về dạng ax+b=0

1. a, \(\frac{5x-2}{3}=\frac{5-3x}{2}\); b, \(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)

c, \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\); d, \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)

e, \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\); f, 4 (0,5-1,5x)=\(\frac{5x-6}{3}\)

g, \(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}+2x\); h, \(\frac{x+4}{5}.x+4=\frac{x}{3}-\frac{x-2}{2}\)

i, \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\); k, \(\frac{5x+2}{6}-\frac{8x-1}{3}=\frac{4x+2}{5}-5\)

m, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\); n, \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right).\frac{1}{3}\left(x+2\right)\)

p, \(\frac{x}{3}-\frac{2x+1}{6}=\frac{x}{6}-x\); q, \(\frac{2+x}{5}-0,5x=\frac{1-2x}{4}+0,25\)

r, \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\); s, \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{6}\)

t, \(\frac{2x-8}{6}.\frac{3x+1}{4}=\frac{9x-2}{8}+\frac{3x-1}{12}\); u, \(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{3}+\frac{2x-1}{12}\)

v, \(\frac{5x-1}{10}+\frac{2x+3}{6}=\frac{x-8}{15}-\frac{x}{30}\); w, \(\frac{2x-\frac{4-3x}{5}}{15}=\frac{7x\frac{x-3}{2}}{5}-x+1\)

Dạng 1: Phương trình bậc nhất

Bài 1: Giải các phương trình sau :

a) 0,5x (2x - 9) = 1,5x (x - 5)

b) 28 (x - 1) - 9 (x - 2) = 14x

c) 8 (3x - 2) - 14x = 2 (4 - 7x) + 18x

d) 2 (x - 5) - 6 (1 - 2x) = 3x + 2

e) \(\frac{x+7}{2}-\frac{x-3}{5}=\frac{x}{6}\)

f) \(\frac{2x-3}{3}-\frac{5x+2}{12}=\frac{x-3}{4}+1\)

g) \(\frac{x+6}{2}+\frac{2\left(x+17\right)}{2}+\frac{5\left(x-10\right)}{6}=2x+6\)

h) \(\frac{3x+2}{5}-\frac{4x-3}{7}=4+\frac{x-2}{35}\)

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

j) \(\frac{x-3}{5}-1=\frac{4x+1}{4}\)

Dạng 2: Phương trình tích

Bài 2: Giải phương trình sau :

a) (x + 1) (5x + 3) = (3x - 8) (x - 1)

b) (x - 1) (2x - 1) = x(1 - x)

c) (2x - 3) (4 - x) (x - 3) = 0

d) (x + 1)² - 4x² = 0

e) (2x + 5)² = (x + 3)²

f) (2x - 7) (x + 3) = x² - 9

g) (3x + 4) (x - 4) = (x - 4)²

h) x² - 6x + 8 = 0

i) x² + 3x + 2 = 0

j) 2x² - 5x + 3 = 0

k) x (2x - 7) - 4x + 14 = 9

l) (x - 2)² - x + 2 = 0

Dạng 3: Phương trình chứa ẩn ở mẫu

Bài 3: Giải phương trình sau :

Giải các phương trình sau:

a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)

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

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

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

e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x-2}\right)\)

f) \(\frac{3}{4x\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)

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

Giải các phương trình sau:

a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)

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

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

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

e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\)

f) \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)

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

bài tập. Giải các pt

1, \(\frac{5}{x-2}+\frac{6}{3-4x}=0\)

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

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

4,\(\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)

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

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

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

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

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

Bài 1. Giải các phương trình sau

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

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

3) \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\)

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

5) \(\frac{5x+3}{12}=\frac{1+2x}{9}\)

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

7) \(\frac{3\left(x-3\right)}{4}+\frac{4x-10,5}{10}=\frac{3\left(x+1\right)}{5}+6\)

8) \(\frac{2\left(3x+1\right)+1}{4}-5=\frac{2 \left(3x-1\right)}{5}-\frac{3x+2}{10}\)

9) \(\frac{x+1}{3}+\frac{3\left(2x+1\right)}{4}=\frac{2x+3\left(x+1\right)}{6}+\frac{7+12x}{12}\)

10) \(\frac{2x-1}{3}-\frac{5x+2}{7}=x+13\)

bài 1 giải phương trình

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

\(\frac{3}{5x-1}+\frac{3}{3-5x}=\frac{4}{\left(1-5x\right)\left(5x-3\right)}\)

\(\frac{3}{1-4x}=\frac{2}{4x+1}-\frac{8+6x}{16x^2-1}\)

\(\frac{5-x}{4x^2-8x}+\frac{7}{8x}=\frac{x-1}{2x\left(x-2\right)}+\frac{1}{8x-16}\)

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