Question

Solve:

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

Answer 1

As you typed it ...

1 + 2x/x+4=3/x-1
1 + 2 + 4 = 3/x - 1
8 = 3/x
8x = 3
x = 3/8

I will assume you meant:
1 + 2x/(x+4) = 3/(x-1)
multiply each term by (x+4)(x-1)

(x+4)(x-1) + 2x(x-1) = 3(x+4)
x^2 + 3x - 4 + 2x^2 - 2x = 3x + 12
3x^2 - 2x - 16 = 0
(3x - 8)(x + 2) = 0
x = 8/3 or x = -2

Can you see how totally critical those brackets are ?