ab-bc+ad-dc/ab+bc+ad+dc

Simplify and state the domain

you probably meant ...

(ab-bc+ad-dc)/(ab+bc+ad+dc)
= (b(a-c) - d(a-c))/(b(a+c) + d(a+c))
= (a-c)(b-d)/((a+c)(b+d))

a ≠ -c , b≠ - d