How Can You Simplify This Boolean Equation Further?

[triden]

Homework Statement

X = A\overline{D}+\overline{B}AC+\overline{B}\overline{D}\overline{C}+BA\overline{C}

Homework Equations

I need to try to simplify or reduce that boolean equation to something as small as possible.

The Attempt at a Solution

It used to be worse and I used a karnaugh map to get to where I am now from a truth table. I am having trouble getting anything better. I can reduce it to get an XOR gate, but I think it can do better. Any tips?

Thanks

 

[story645]

de morgan's law, double negation, tautologies, and logic properties
http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Logic/Logic2.html

 

[snarfherder]

You can reduce gate inputs by collecting terms, but this is as simplified as it gets. Draw the k-map. A(B xor C + D') + B'C'D'