Question 993433
You don't say by what method, it can be solved completing the squares or using the quadratic formula. Here is completing the squares:

Solve for x: 
1/x+1/(x-1)=2/(x^2-2x) Rewrite for convenience: 1/(x-1)+1/x= 2/(x^2-2x)
Look for a polynomial to multiply both sides in order to get rid of fractions,
multiply by (x-1) (x^2-2x):
(x-2)(x-1)-2x+x^2 = 2(x-1)
Expand out terms of the left hand side:
2x^2-5x+2= 2(x-1)
Expand out the right hand side:
2 x^2-5 x+2 = 2 x-2
Subtract 2x-2 from both sides:
2x^2-7x+4 = 0
Divide both sides by 2 to simplify:
x^2-(7 x)/2+2= 0
Solve the quadratic equation by completing the square.
Subtract 2 from both sides:
x^2-(7x)/2 = -2
Take one half of the coefficient of x and square it, then add it to both sides.
Add 49/16 to both sides:
x^2-(7x)/2+49/16= 17/16
Factor the left hand side.
(x-7/4)^2 = 17/16
Now eliminate the exponent on the left hand side by taking th sq rt both sides:
x-7/4= sqrt(17)/4 or x-7/4= -sqrt(17)/4
Now solve each equation separately:
x-7/4= sqrt(17)/4
Add 7/4 to both sides:
x = 7/4+√(17)/4 or x-7/4 = -√(17)/4
Look at the second equation:  Solve for x.
Add 7/4 to both sides:
x= 7/4+√(17)/4 or x= 7/4-√(17)/4