To simplify the expression, we can use the trigonometric identity:

sin$\alpha$ - sin$\beta$ = 2sin$(\alpha -\beta )/2$cos$(\alpha +\beta )/2$

cos$\alpha$ - cos$\beta$ = -2sin$(\alpha +\beta )/2$sin$(\alpha -\beta )/2$

So, the given expression becomes:

$2sin(5\pi /18)cos(6\pi /18)$ / $-2sin(6\pi /18)sin(5\pi /18)$ = $2sin(5\pi /18)cos(\pi /3)$ / $-2sin(\pi /3)sin(5\pi /18)$ = $2sin(5\pi /18)<em>1/2$ / $-\surd 3/2</em>sin(5\pi /18)$ = -1/√3

Therefore, $sin(11\pi /18)-sin(\pi /18)$ / $cos(11\pi /18)-cos(\pi /18)$ simplifies to -1/√3.