Either perform the indicated operation or solve....whichever is appropriate?

Question

-2/x=3/x+2

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

Answer 1

-2/x = 3/(x+2)
-2(x+2) = 3x
-2x - 4 = 3x
5x = -4
x = -4/5



times by x-2
3(x-2) + 1 = 2x-3
3x - 6 + 1 = 2x - 3
3x -5 = 2x - 3
3x - 2 = 2x
-2 = -x
x = 2

Answer 2

1. -2/x = 3/x+2 -> -5/x = 2 -> x = -5/2

2. Do you mean 3 + (1/(x-2)) = (2x-3)/(x-2) or 3 + (1/(x-2)) = 2x - (3/(x-2))

In both cases multiply by (x-2)

a. 3(x-2) + 1 = (2x-3) -> 3x - 2x = 6 - 1 - 3 -> x=2
b. 3(x-2) + 1 = 2x(x-2) - 3 -> 3x - 6 + 1 = 2x^2 - 4x - 3 -> 2x^2 -7x + 2 = 0 and this is solvable only by x = ((-b +/- sqrt(b^2 - 4ac))/4a

Take your pick

Please note, it is +2 NOT -2 as in previous answer. 6-4=2.

Answer 3

I can't tell what the demonimator is:
-2/x=3/(x+2)
-2(x+2) = 3x
-2x -4 = 3x
-4 = 5x
-.8 = x

OR
-2/x = 3/x + 2
-2 = 3 + 2x
-5 = 2x
-2.5 = x

3+1/(x-2) = (2x-3)/(x-2)
3(x-2) + 1 = 2x - 3
3x - 6 + 1 = 2x - 3
x = 2 - doesn't work because that would be dividing by zero

OR
3 + 1/(x-2) = 2x - 3/(x-2)
4/(x-2) = 2x - 3
4 = (2x-3)(x-2)
4 = 2x^2 - 7x + 6
0 = 2x^2 - 7x -2

Answer 4

Hello
I assume that the x+2 is all in the denominator!
Multiply the first one by x(x+2) giving us

-2(x+2) = 3x so we have -2x -4 = 3x or -4 = 5x so x = -4/5

Is the 2x-3 all in the numerator or just the 3. Please use parans where needed.

Thank You!

Answer 5

-2/x = 3/(x+2)
-2(x+2) = 3x
-2x - 4 = 3x
5x = -4
x = -4/5

3 + 1/(x-2) = (2x-3)/(x-2)
3(x-2) + 1 = 2x - 3
3x - 6 + 1 = 2x - 3
x = 2