NAND Simplified with xy + !x z
Three hints that can solve this:


You can implement an inverter by either a NAND or a NOR gate with both inputs connected to the same signal.
You can put bubbles on both ends of a wire without changing the circuit function.
An AND gate with both inputs inverted is equivalent to a NOR gate, and an OR gate with both inputs inverted is equivalent to a NAND gate. Graphically, this can be thought of as "pushing the bubbles through" the gate, leaving one bubble on the output and changing the type of gate. Or, in symbols \$\bar{A}\bar{B} =\overline{A+B}\$.