Question 541161
{{{6/t^3-9t^5+3}}} (as you wrote it) is not a polynomial. 
Just in case, {{{6/(t^3-9t^5+3)}}} is not a polynomial either. 
(Negative exponents and variables in denominators are not allowed in polynomials).
So degree is not defined for such expressions.
As you wrote it, there is no equal sign, so there is no "other side."
If it were polynomial {{{6t^3-9t^5+3}}}, the leading coefficient would be -9 and the degree would be 5, like you thought.
{{{y=6/(t^3-9t^5+3)}}} and {{{y=6/t^3-9t^5+3}}} are rational functions.
My guess is that you are taking an online course, and someone messed up when entering the questions and answers. As one of my sons attended an online charter school, I am familiar with that phenomenon. (I assume that typos happen in printed problems given to students in brick-and-mortar schools, too, but I could not see every mistake that happened in school when my children attended them).