\(\displaystyle (A \backslash B) \cap (A \cap B)'\)

\(\displaystyle = (A \cap B') \cap (A' \cup B')\)

\(\displaystyle = A \cap B' \cap (B' \cup A')\)

\(\displaystyle = A \cap B'\)

Where we used the following rules...

\(\displaystyle (A \backslash B) = (A \cap B')\)

\(\displaystyle (A \cap B)' = (A' \cup B')\)

\(\displaystyle B' \cap (B' \cup A') = B'\)