Answer
$ -\displaystyle \frac{1}{c+d },\quad a\neq b$
Work Step by Step
To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
= $\displaystyle \frac{b-a}{ac+ad-bc-bd}$
... factor the denominator in pairs,
... $ac+ad-bc-bd=a(c+d)-b(c+d)=(a-b)(c+d)$
... now, we factor out -1 in the numerator to get common factors
= $\displaystyle \frac{-(a-b)}{(a-b)(c+d)}$
... common factors cancel,
... exclude the possibility that $a-b=0.$
= $\displaystyle \frac{-1}{c+d},\quad a\neq b$
=$ -\displaystyle \frac{1}{c+d },\quad a\neq b$