Solve the equation X-1 / 1-10% = x-0.9/0.92

Solve the equation X-1 / 1-10% = x-0.9/0.92

The original equation is 10x-10 / 9 = 100x-90 / 92
9*(100x-90)=92*(10x-10)
900x-810=920x-920
110=20x
x=2/11