what is the answer to; x^2-3x/x+1=4/x+1?

x= 4 and also x = -1

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

x + 1 = 0
x = -1

x - 4 = 0
x = 4

∴ x = -1 , 4

if it is set up like
x2-3x/(x+1)=4/(x+1)
take out a common factor of x+1 and set it equal to zero
x+1=0
x=-1

x2-3x=4
get four on the same side as x squared and three x
x2-3x-4=0
set it up as below
(x-4)(x+1)=0
set each term to zero
x-4=0
x=4
x+1=0
x=-1
so x= -1, 4

As given , question reads as :-
x² - 3x/(x + 1) = 4/(x + 1)
x²(x + 1) - 3x = 4
x³ + x² - 3x - 4 = 0
x = 1.83 , x = - 1.42 (by calculator)

HOWEVER it may be that you mean :-
(x² - 3x) / (x + 1) = 4 / (x + 1)
x² - 3x = 4
x² - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = 4 , x = - 1

Note
Question, AS GIVEN, could ALSO be read as :-
x² - (3x/x) + 1 = (4/x) + 1

AT this level you should be presenting questions clearly by using BRACKETS.

0 is the answer to this query.........