Question

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

h) \(\frac{12x+1}{6x-2}-\frac{9x-5}{3x+1}=\frac{108x-36x^2-9}{4\left(9x^2-1\right)}\)

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

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

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