NAND Simplified with xy + !x z

I've been trying to work on a few problems, though I'm not sure how to rewrite this a few circuits using only NAND/NOR -->

an example is shown below;

How am I able to rewrite only using NAND + NOR gates if anyone is able to help me on this.

Thank you.

• Hint: if you put bubbles on both ends of a wire, it doesn't change the circuit function. – The Photon Jan 10 at 6:21
• @The Photon I'm sorry, I posted the wrong problem. I had already done that one earlier by reduction I will update the picture now – user209499 Jan 10 at 6:24
• OK, you should still be able to solve this using the rules in my answer. – The Photon Jan 10 at 17:51

3. 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}\$$.