Question 54815
First off, if your boyfriend puts the time he will propose to you in an algebraic form, I think you should reject him for being a tool. That being said, lets get to the math:

We've got

{{{(p^2+3p+2)/(p+1) = 3/2 +3p -3}}}

if you factor the top left part (I'm assuming you're cool with factoring), you get:

{{{((p+1)(p+2))/(p+1) = 3/2 +3p -3}}}

the {{{p+1}}} terms on the left cancel out, and you've got

{{{p+2 = 3/2 + 3p - 3}}}

I'll combine the number terms on the right

{{{p+2 = 3p - 3/2}}}

Ok, I'll subtract a p from each side

{{{2 = 2p - 3/2}}}

and add 3/2 to each side

{{{7/2 = 2p}}}

Divide by two

{{{7/4 = p}}}


I got what you got. 

Is there a chance this thing was copied down wrong? I somewhat expected there to be a {{{p^2}}} somewhere on the right instead of two constant terms. What happens if you never solve this? Are you doomed to be single?