I have two conic equations that I've been unable to put in standard form without getting at least one fraction, which messes up the rest of the steps.

The first:

I know this is an ellipse because the and terms have the same sign.

I need to put it in the standard form = 1 by factoring out terms and completing the square:

Completing the square causes this issue with the fraction in the x term:

Halving -3 and squaring it gets the fraction , so I get:

The right side simplifies to:

The y expression is an easy perfect square, so I get:

I can't get the x expression into a perfect square, and I've tried multiple approaches such as:

Dividing both sides by yields even more of a fraction mess, and I still can't get the numerators and isolated.

The second: --a hyperbola

After putting these in standard form, I need to find the center, vertices and foci--but I obviously can't do this until they're in standard form. Sorry about the length of this post, but I wanted to add everything I've tried so far. I'm about at my wit's end with these, so any help would be awesome!

Thanks