Giải các phương trình sau:
a) \(\left(\frac{x-2}{x-1}\right)^2-5\left(\frac{x+2}{x+1}\right)^2+4\left(\frac{x^2-4}{x^2-1}\right)=1\)
b) \(\left(\frac{x-1}{x}\right)^2+\left(\frac{x-1}{x-2}\right)^2=\frac{40}{9}\)
c) \(x.\frac{4-x}{x+2}.\left(\frac{8-2x}{x+2}\right)=3\)
d) \(\frac{1}{3x-2020}+\frac{1}{4x-2018}+\frac{1}{5x-2017}=\frac{1}{12x-2019}\)
Giải các phương trình sau
a) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{15}{\left(x+1\right)\left(2-x\right)}\)
b) \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)
c) \(\frac{6}{x-1}-\frac{4}{x-3}=\frac{8}{2x-6}\)
d) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
e) \(\frac{1}{x-2}+\frac{5}{x+1}=\frac{3}{2-x}\)
f) \(\frac{5x}{2x+2}+1=-\frac{6}{x+1}\)
g) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)
h) \(\frac{3x}{x-2}-\frac{x}{x-5}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)
Giải các bất phương trình sau :
a) \(15-2x\left(1-x\right)< 2x^2-4x+5\)
b) \(x^2-\frac{x\left(3x+2\right)}{3}< \frac{x-6}{3}\)
c) \(1+\frac{x+4}{3}< x-\frac{x-3}{2}\)
d) \(\left(\frac{2x+1}{2}\right)^2+\frac{3x\left(1-x\right)}{3}-\frac{5x}{4}\le1\)
giải các phương trình sau :
a. (x-3)(x-4)-2.(3x-2)=\(\left(4-x\right)^2\)
b. \(\left(x+2\right)\left(x-2\right)+5x^2=\left(3x+1\right)-3x^2\)
c. \(\left(x+2\right)^3-\left(x-1\right)^3=\left(3x+1\right).\left(3x-1\right)\)
d.\(\frac{3-x}{2018}+\frac{x-1}{2020}=\frac{-x}{2021}+1\)
bài 1 giải phương trình
\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)
\(\frac{3}{5x-1}+\frac{3}{3-5x}=\frac{4}{\left(1-5x\right)\left(5x-3\right)}\)
\(\frac{3}{1-4x}=\frac{2}{4x+1}-\frac{8+6x}{16x^2-1}\)
\(\frac{5-x}{4x^2-8x}+\frac{7}{8x}=\frac{x-1}{2x\left(x-2\right)}+\frac{1}{8x-16}\)
\(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^2-x+1}=\frac{3}{x\left(x^4+x^2+1\right)}\)
Bài 3 : Giải các phương trình sau bằng cách đưa về dạng ax+b=0 :
a) \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
b) \(4\left(0,5-1,5x\right)=-\frac{5x-6}{3}\)
c) \(\frac{x+4}{5}-x+4=\frac{x}{3}-\frac{x-2}{2}\)
d) \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\)
e) \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right)-\frac{1}{3}\left(x+2\right)\)
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, \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)
Bài 3: Giải các phương trình sau bằng cách đưa về dạng ax+b =0 :
a) \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\)
b) \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{5}\)
c) \(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x-1\right)}{7}-5\)
d) \(14\frac{1}{2}-\frac{2\left(x+3\right)}{5}=\frac{3x}{2}-\frac{2\left(x-7\right)}{3}\)
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) \(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}\)
Giải các phương trình sau
a) \(\frac{7x-3}{x-1}=\frac{2}{3}\)
b) \(\frac{2\left(3-7x\right)}{1+x}=\frac{1}{2}\)
c) \(\frac{1}{x-2}+3=\frac{3-x}{x-2}\)
d) \(\frac{8-x}{x-7}-8=\frac{1}{x-7}\)
e) \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
f)\(\frac{1}{x-1}+\frac{2}{x+1}=\frac{x}{x^2-1}\)
g) \(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
h)\(5+\frac{76}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
i) \(\frac{90}{x}-\frac{36}{x-6}=2\)
k) \(\frac{1}{x}+\frac{1}{x=10}=\frac{1}{12}\)
l) \(\frac{x+3}{x-3}-\frac{1}{x}=\frac{3}{x\left(x-3\right)}\)
m) \(\frac{3}{x+2}-\frac{2}{x-2}+\frac{8}{x^2-4}=0\)
n) \(\frac{3}{x+2}-\frac{2}{x-3}=\frac{8}{\left(x-3\right)\left(x+2\right)}\)
o)\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
p) \(\frac{x}{x+1}-\frac{2x-3}{1-x}=\frac{3x^2+5}{x^2-1}\)
q) \(\frac{5}{x+7}+\frac{8}{2x+14}=\frac{3}{2}\)
r) \(\frac{x-1}{x}=\frac{1}{x+1}=\frac{2x-1}{x^2+x}\)
