unequal and unknown variances


New Member
We have a question on our homework that asks us to discuss the difficulty with unknown and unequal variances with respect to a t-distribution. I wrote out the big 'ol formula with the Z~N(0,1) on top and the sum of 2 chi-squared distributions (one for each of the RV's) on the bottom. I'm not sure if I got it right and I don't know what I'm looking for anyway.
Any guidance will be appreciated.
I'm also a little unclear about why we divide the chi-squared distribution in the denominator by (n-1). It looks to me like it was just thrown in to cancel the (n-1) in the numerator. Why can you do that? I have searched through my book, but I can't find the why.