Giải phương trình sau:
a) \(\frac{x-1}{x-2}+\frac{x+3}{x-4}=\frac{2}{\left(x-2\right)\left(4-x\right)}\)
b) \(\frac{7x-3}{x-x^3}=\frac{1}{x-1}-\frac{5}{x\left(x-1\right)}\)
c) \(\frac{15}{x^2+x-12}+\frac{2}{x-3}=\frac{1}{x+4}\)
d) \(\frac{3}{x-2}+\frac{3}{x-3}-\frac{1}{x^2-5x=6}=3\)