In-between fractions

Mathematica, 16 bytes

Range@##⋃{#2}&

An unnamed function that takes two integers and a rational number and returns a list of numbers, e.g.:

Range@##⋃{#2}&[-2, 3, 1/2]
(* {-2, -(3/2), -1, -(1/2), 0, 1/2, 1, 3/2, 2, 5/2, 3} *)

Mathematica's Range does exactly what the challenge asks, except that it omits the upper bound if the difference between lower and upper bound isn't exactly a multiple of the step size. Therefore we take the Union (using ⋃) with the list containing only the upper bound which ensures that it appears exactly once. Note that Union will sort the result but we want it sorted anyway, since the step size is always positive. Also since we're working with rationals, they're automatically reduced as much as possible.

T-SQL 2012+, 831 535 477 270 246 240 219 bytes

Please note this is a one liner - sql doesn't have build in function to reduce the fraction. May not be the best language for this type of question. It is human readable(kind of - compared to some of the other languages).

DECLARE @f INT=-5,@t INT=3,@n INT=3,@ INT=8;

WITH C as(SELECT
top((@t*@-@f*@)/@n+1)ROW_NUMBER()OVER(ORDER BY @)M
FROM sys.messages)SELECT(SELECT
IIF(V%@=0,LEFT(V/@,9),CONCAT(V/MAX(M),'/',ABS(@)/MAX(M)))FROM c
WHERE V%M=0AND @%M=0)FROM(SELECT
@f*@+@n*~-M V FROM c)k

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Python 2, 81 bytes

from fractions import*
a,b,c=map(Fraction,input())
while a<b:print a;a+=c
print b

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