18/4x-1 - 1/x+1 = 1

Assuming that the problem is:  18/(4x - 1) - 1/(x + 1)  =  1

Multiply both sides by (4x - 1)(x + 1):  

18(4x - 1)(x + 1)/(4x - 1) - 1(4x - 1)(x + 1)/(x + 1)  =  1(4x - 1)(x + 1)

18(x + 1) - (4x - 1)  =  4x² + 3x - 1

18x + 18 - 4x + 1  =  4x² + 3x - 1

14x + 19  =  4x² + 3x - 1

0  =  4x² - 11x - 20

Factor:  (4x + 5)(x - 4)  =  0

x  =  -5/4  or  x = 4