First, multiply the fraction on the left by this form of #1#: #(-1)/-1#:
#(-1)/-1 xx k/(d - b) => (-k)/(-(d - b)) => (-k)/(-d + b) => -k/(b - d)#
We can now rewrite the expression as:
#(-k)/(b - d) -: b/(b - d) => ((-k)/(b - d))/(b/(b - d))#
We can now use this rule for dividing fractions to evaluate the expression:
#(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)(-k)/color(blue)(b - d))/(color(green)(b)/color(purple)(b - d)) =>#
#(color(red)(-k) xx color(purple)((b - d)))/(color(blue)((b - d)) xx color(green)(b)) =>#
#(color(red)(-k) xx cancel(color(purple)((b - d))))/(cancel(color(blue)((b - d))) xx color(green)(b)) =>#
#color(red)(-k)/color(green)(b)#
And we need to ensure from the original expression that
#b != d#
to ensure we do not divide by #0#
