It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:-
a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and x can never be equal to a whole no.
Prove the above theorem right or wrong.
$\frac{a}{b} + c = \frac{bc + a}{b}$.
Since $b$ is even, $bc$ is even. So, $bc + a$ is odd.
Note that $x$ cannot be an integer because $a$ is odd while $b$ is even so $b \nmid a$. Thus, since $c$ is an integer, $x$ is never an integer.