To simplify the expression 3z^5+5z^4+z+5/z+2, we can start by simplifying the expression inside the fraction:
3z^5+5z^4+z+5/z+2 = (3z^5+5z^4+z+5) / (z+2)
Next, we can use the fact that the same term can be added to both the numerator and the denominator of a fraction without changing the value of the fraction:
(3z^5+5z^4+z+5) / (z+2) = ((3z^5+5z^4+z+5) + (z+2) - (z+2)) / (z+2)
This simplifies to:
((3z^5+5z^4+z+5) + (z+2) - (z+2)) / (z+2) = (3z^5+5z^4+z+5-z-2) / (z+2)
Then, we can simplify the expression inside the parentheses:
(3z^5+5z^4+z+5-z-2) / (z+2) = (3z^5+5z^4+z-z-2) / (z+2) = (3z^5+5z^4-2) / (z+2)
Finally, we can use the fact that the same term can be added to or subtracted from both the numerator and the denominator of a fraction without changing the value of the fraction:
(3z^5+5z^4-2) / (z+2) = ((3z^5+5z^4-2) + 2 - 2) / (z+2) = (3z^5+5z^4) / (z+2)
Therefore, the simplified form of the expression 3z^5+5z^4+z+5/z+2 is (3z^5+5z^4) / (z+2).