First, rewrite the expression as:
#((6x - 6)/5)/((x - 1)/15)#
Next, use this rule for dividing fractions to rewrite the expression again:
#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#
#(color(red)(6x - 6)/color(blue)(5))/(color(green)(x - 1)/color(purple)(15)) => (color(red)((6x - 6)) xx color(purple)(15))/(color(blue)(5) xx color(green)((x - 1))) => color(red)((6(x - 1)) xx color(purple)(15))/(color(blue)(5) xx color(green)((x - 1))) =>#
#(color(red)(6cancel((x - 1))) xx cancel(color(purple)(15))3)/(cancel(color(blue)(5)) xx color(green)(cancel((x - 1)))) => 18#
However, we need to ensure we do not divide by #0#. Therefore, the exclude value is when:
#(x - 1)/15 = 0# so #x != 1#
