Metaphor or Simile?

To laughter and contempt; that she may feel
How sharper than a serpent's tooth it is
To have a thankless child! Away, away!

What two things are being compared?

Right. And without the use of "like" or "as," it's considered a metaphor.

It's a metaphor.

http://www.englishclub.com/vocabulary/figures-simile.htm

Okay i understand how it would not be a simile but how would it be a metaphor??

serpents tooth and thankless child?

Gracias

De nada!