Python Friendly Form
Overall, the code is very good, but a few tiny improvements can be made:


In the decompose function x = x - m can be replaced with x -= m
Instead of return decompose(x) + [m] and such, use yield
Instead of for a in answer ..., use print(*answer, sep='\n')
In the decompose function, math.ceil(float(1 / x)) can be changed to math.ceil(1 / x). Python 3.x automatically interprets / as a float operator
As only math.ceil is used, you could just do from math import ceil


Here's the final code:

from math import ceil
from fractions import Fraction

def decompose(x):
    if x.numerator == 1:
        yield x
        return 

    m = Fraction(1, ceil(1 / x))
    x -= m

    yield m
    yield from decompose(x)

def main():
    inp = input("Enter positive fraction in form 'a/b': ")

    try:
        x = Fraction(inp)

    except ValueError:
        print("Invalid input.")
        return

    if float(x) == 0:
        print("Enter non-zero value.")
        return

    if float(x) &lt; 0:
        print("Converting to positive value.")
        x = -x

    if float(x) &gt;= 1:
        print("Enter valid fraction")
        return

    print(*decompose(x), sep='\n')

if __name__ == "__main__":
    main()


Hope this helps!