a)
\frac{3}{x-2}-\frac{1}{x-2}=5
\frac{3-1}{x-2}=5
\frac{2}{x-2}=\frac{5}{1}
5*(x-2)=2*1
5x-10=2
5x=12
x=\frac{12}{5}
x=2\frac{2}{5}
b)
6+\frac{1}{x-1}=-\frac{2}{x+1}
\frac{6(x-1)+1}{x-1}=\frac{-2}{x+1}
\frac{6x-6+1}{x-1}=\frac{-2}{x+1}
\frac{6x-5}{x-1}=\frac{-2}{x+1}
(6x-5)(x+1)=-2(x-1)
6x^2+6x-5x-5=-2x+2
6x^2+x-5+2x-2=0
6x^2+3x-7=0
a=6, b=3, c=-7
\Delta=b^2-4ac=9-4*6*(-7)=9+168=177
\sqrt\Delta=\sqrt{177}
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-3-\sqrt{177}}{2*6}=\frac{-3-\sqrt{177}}{12}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-3+\sqrt{177}}{2*3}=\frac{\sqrt{177}-3}{6}