Các khẳng định sau đây đúng hay sai :

a) Phương trình \(\dfrac{4x-8+\left(4-2x\right)}{x^2+1}=0\) có nghiệm là \(x=2\)

b) Phương trình \(\dfrac{\left(x+2\right)\left(2x-1\right)-x-2}{x^2-x+1}=0\) có tập nghiệm là \(S=\left\{-2;1\right\}\)

c) Phương trình \(\dfrac{x^2+2x+1}{x+1}=0\) có nghiệm là \(x=-1\)

d) Phương trình \(\dfrac{x^2\left(x-3\right)}{x}=0\) có tập nghiệm là  \(S=\left\{0;3\right\}\)

Giải các phương trình sau :

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

b) \(1+\dfrac{x}{3-x}=\dfrac{5x}{\left(x+2\right)\left(3-x\right)}+\dfrac{2}{x+2}\)

c) \(\dfrac{2}{x-1}+\dfrac{2x+3}{x^2+x+1}=\dfrac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)

d) \(\dfrac{x^3-\left(x-1\right)^3}{\left(4x+3\right)\left(x-5\right)}=\dfrac{7x-1}{4x+3}-\dfrac{x}{x-5}\)

Giải các phương trình sau:

a) \(x^2+\dfrac{2x}{x-1}=8\)

b) \(\dfrac{x^2+2x+1}{x^2+2x+2}+\dfrac{x^2+2x+2}{x^2+2x+3}=\dfrac{7}{6}\)

c) \(\dfrac{x+4}{x-1}+\dfrac{x-4}{x+1}=\dfrac{x+8}{x-2}+\dfrac{x-8}{x+2}+6\)

d) \(\left(x^2+6x+8\right)\left(x^2+8x+15\right)=24\)

e) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)=28\)

f) \(3\left(-x^2+2x+3\right)^4-26x^2\left(-x^2+2x+3\right)^2-9x^4=0\)

g) \(x^4+6x^3+11x^2+6x+1=0\)

h) \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2=0\)

i) \(\left(x+2\right)^4+\left(x+8\right)^4=272\)

Giải các phương trình sau :

a) \(\dfrac{9x-0,7}{4}-\dfrac{5x-1,5}{7}=\dfrac{7x-1,1}{3}-\dfrac{5\left(0,4-2x\right)}{6}\)

b) \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}=1-\dfrac{4}{\left(x-1\right)\left(x+3\right)}\)

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

d) \(\dfrac{8x^2}{3\left(1-4x^2\right)}=\dfrac{2x}{6x-3}-\dfrac{1+8x}{4+8x}\)

Giải các phương trình sau :

a) \(\dfrac{5\left(x-1\right)+2}{6}-\dfrac{7x-1}{4}=\dfrac{2\left(2x+1\right)}{7}-5\)

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

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

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

Giải các phương trình :

a) \(\dfrac{1}{2x-3}-\dfrac{3}{x\left(2x-3\right)}=\dfrac{5}{x}\)

b) \(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)

c) \(\dfrac{x+1}{x-2}+\dfrac{x-1}{x+2}=\dfrac{2\left(x^2+2\right)}{x^2-4}\)

d) \(\left(2x+3\right)\left(\dfrac{3x+8}{2-7x}+1\right)=\left(x-5\right)\left(\dfrac{3x+8}{2-7x}+1\right)\)

Giải các phương trình :

a) \(\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\)

b) \(\dfrac{3}{\left(x-1\right)\left(x-2\right)}+\dfrac{2}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)

c) \(1+\dfrac{1}{x+2}=\dfrac{12}{8+x^3}\)

d) \(\dfrac{13}{\left(x-3\right)\left(2x+7\right)}+\dfrac{1}{2x+7}=\dfrac{6}{\left(x-3\right)\left(x+3\right)}\)