Help me with this math problem (algebra)?

Question

Here it is. Please show your work. I'm stuck. Solve the equation:
2/x^2-1 - 1/x-1 = 1

Answer 1

The given equation is 2/x^2 - 1 - 1/x  - 1 = 1

2/(x^2)  - 1/x  - 2 = 1

Lcm of x^2 and x is x^2.

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

Multiply each side by x^2.

2 - x - 2x^2 = x^2

Subtract x^2 to each side.

2 - x - 2x^2 -  x^2 = x^2 - x^2

-3x^2 - x + 2 = 0

Multiply each side by negative one.

3x^2 + x - 2 = 0

3x^2 + 3x - 2x- 2 = 0

3x(x + 1) -1(x+1) = 0

Take out common factors.

(3x -1) or (x +1)  = 0

3x - 1 = 0 or x + 1 = 0

3x = 1  or  x = -1

x = 1/3 or  x = -1

The solutions are x = -1and x = 1/3.

Comments

3x^2 + x - 2 = 0

3x^2 + 3x - 2x- 2 = 0

3x(x + 1) -2(x+1) = 0

Take out common factors.

(3x -2) or (x +1)  = 0

3x - 2 = 0 or x + 1 = 0

3x = 2  or  x = - 1

x = 2/3 or  x = - 1

The solutions x = -1 and x = 2/3.