Cannot get this solution!!! (x-2)/(x) + (1/2)= (x+1)/(x-2)

Answer 1

(x-2)/(x) + (1/2)= (x+1)/(x-2)
Assume x≠0 and x≠2.

Add the two terms on the left using the common denominator of x.

[2(x-2)+x]/2x = (x+1)/(x-2)
(3x-4)/2x = (x+1)/(x-2)
Cross multiply:
(3x-4)(x-2) = 2x(x+1)
3x²-10x+8 = x²+x
x²-12x+8 = 0
x=(12±sqrt(112))/2

Answer 2

Simplifies to
x=6±2sqrt(7)