x - 1/x = 77/18
multiply by the common denominator 18x
18x(x - 1/x )= 77/18 *18x
distribute
18x^2 -18 = 77x
subtract 77 x from each side
18x^2 -77x-18=0
factor
(2 x - 9) (9 x + 2) = 0
using the zero property
2x-9 =0 9x+2 =0
2x=9 9x=-2
x = 9/2 x = -2/9
x cannot = 9/2 because this is not a proper fraction in the lowest terms
so x = -2/9
