Question

i need to solve this rational expression:
3/x + 4/x+2 = -1/x

Answer 1

I assume the problem is as follows:

(3/x) + (4/x) + 2 = (-1/x)
3/x + 4/x +1/x = -2
8/x = -2
8 = -2x Rearranging this to get:

-2x = 8
x = -4

Answer 2

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

Answer 3

-4

Answer 4

{3(x+2) +4x}/ x(x+2) = -1(x+2)/x(x+2)
Cancelling 1/ x(x+2),

3(x+2) + 4x = -1(x+2)
3x + 6 + 4x = -x - 2
8x = -8
x = -1

Answer 5

x=-4

Answer 6

@shine & bbv1814 - Try substituting the values:

p(-1) : LHS = 3/-1 + 4/ (-1+2) = -3 + 4 = 1
RHS = -1/-1 = 1
Therefore, LHS = RHS so the solution x = -1 is true.

If you use x = -4, LHS = 3/-4 + 4/ (-4+2) = -3/4 -2 = -11/4
RHS = -1/-4 = 1/4

Clearly, LHS is not equal to RHS so x = -4 is not a solution

Answer 7

Since the problem is not as I assumed orginally but has been clarified, then the solution is different which is the following:

3/x + 4/(x+2) = -1/x Multiply both sides by x and you get:
3 + 4x/(x+2) = -11 Multiply both sides by (x+2) and you get:
3(x+2) +4x = -1(x+2)
3x + 6 +4x = -x-2
7x + 6 = -x-2
8x = -8
x = -1