Solve:

1+2x/x+4=3/x-1

Assuming you mean

(1+2x)/(x+4) = 3/(x-1)
(1+2x)(x-1) = 3(x+4)
2x^2 - x - 1 = 3x + 12
2x^2 - 4x - 13 = 0

Now it's just a regular old quadratic equation to solve.

Note that right from the beginning you have to exclude -4 and 1 from the domain.