Math help please Quadratic Equations?

Question

Solve-
X+2/x^2-2 = 2/3-x
could you show me how you get the answer please?

Answer 1

ill give it a shot - im not sure , anyways i got 2 answers..

(1st)

(3-x)x+2 = 2 (x^2-2)

3x-x^2+6-2x = 2x^2-4

x-x^2+6 = 2x^2-4

x-1/x+6 = 2/x-4

x-1+6x = 2-4x

x+4x+6x = 2+1

11x = 3

x = 3/11


(2nd possible answer)


(3-x)x+2 = 2 (x^2-2)

3x-x^2+6-2x = 2x^2-4

x-x^2+6 = 2x^2-4

x-1/x+6 = 2/x-4

x-1+6/x = 2-4/x

-5 = -2/x

-5x = -2

x = -2+5

x = 3

Answer 2

It looks to me like the equation should be written as :
(x + 2) / (x^2 - 2) = 2 / (3 - x)
Brackets are extremely important in single line equations, otherwise we're open to misinterpretation.

Cross-multiplying the above equation gives :
(x + 2)(3 - x) = (x^2 - 2)(2)

Multiplying out gives :
3x - x^2 + 6 - 2x = 2x^2 - 4

Adding like terms, transferring and rearranging gives :
3x^2 - x - 10 = 0

Factorising gives :
(x - 2)(3x + 5) = 0

Expressing each factor equal to zero gives :
x = 2 or -5/3

Answer 3

multiply by x^2 on both sides to get rid of the x^-2
x^3-2x^2+2=(2x^2)/3-x^3
(8x^2)/3=2
x=(+-)(3/4)^.5
(i don't think we're missing an awnser)