X/x-2+x-1/x+1=-1

I'm having trouble figuring this out, an explanation on how to solve would suffice.

x = sqrt (5) / 2 - 1/2 or x = - 1/2 - sqrt (5) / 2

Step-by-step explanation:

Solve for x over the real numbers:

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

x - 2 + x/x + 1 - 1/x = x - 1/x:

x - 1/x = - 1

Bring x - 1/x together using the common denominator x:

(x^2 - 1) / x = - 1

Multiply both sides by x:

x^2 - 1 = - x

Add x to both sides:

x^2 + x - 1 = 0

Add 1 to both sides:

x^2 + x = 1

Add 1/4 to both sides:

x^2 + x + 1/4 = 5/4

Write the left hand side as a square:

(x + 1/2) ^2 = 5/4

Take the square root of both sides:

x + 1/2 = sqrt (5) / 2 or x + 1/2 = - sqrt (5) / 2

Subtract 1/2 from both sides:

x = sqrt (5) / 2 - 1/2 or x + 1/2 = - sqrt (5) / 2

Subtract 1/2 from both sides:

Answer: x = sqrt (5) / 2 - 1/2 or x = - 1/2 - sqrt (5) / 2