\frac{13}{x-3}-\frac{3}{x+1}<-4
x\ne 3 , x\ne-1
\frac{13}{x-3}-\frac{3}{x+1}+4<0
\frac{13(x+1)-[3(x-3)]+4(x-3)(x+1)}{(x-3)(x+1)}<0
\frac{13x+13-(3x-9)+4(x^2+x-3x-3)}{(x-3)(x+1)}<0
\frac{13x+13-3x+9+4x^2+4x-12x-12}{(x-3)(x+1)}<0
\frac{4x^2+2x+10}{(x-3)(x+1)}<0 /*(x-3)^2(x+1)^2
(4x^2+2x+10)(x-3)(x+1)<0
4x^2+2x+10=0
a=4, b=2, c=10
\Delta=b^2-4ac=4-4*4*10=4-160=-156<0 brak rozwiązań
lub
x-3=0
x=3
lub
x+1=0
x=-1
x\in (-1;3)