Express (a^2+ab-ac-bc)÷a^2-c^2 over a-b
in single fraction.
Answer is
a^2-b^2 over a+c
How the steps?
a^2+ab-ac-bc
= a(a+b)-c(a+b)
= (a-c)(a+b)
(a^2-c^2)/(a-b) = (a-c)(a+c)/(a-b)
Now do the division (multiply by the reciprocal) and the (a-c) factors cancel, leaving
(a+b)(a-b)/(a+c)
= (a^2-b^2)/(a+c)