Unlike some other that can do this one in there heads, I have to workout it out visually, I used the ration test, I believe I may have made some mistakes in simplification so I am asking for a check like always.

Doing some simplification to

Multiplying out the terms in the numerator and denominator gave me a fraction with the same degree in both denominator and numerator

I can take the ratio of the degrees of the highest powers since they the same to find limit which gives and the ratio test states, if the limit is less than 1, the series converges, is this correct?

I just got confused when wolfram, simplified the series to and stated it diverges, I was using wolfram for a quick check, If I did things correct or not.