equation is
a +b x / c+d x = 3 +4 x / 5+6 x where a,b,c,d are constants
So by comparing can we say that
a=3,b=4,c=5,d=6?
They are not the only solutions. See ibdutt's post for a second solution. The complete solution set is a = 3n, b = 4n, c = 5n, and d = 6n where n is any (non-zero) real number.=:
$\displaystyle \frac{(3n) + (4n)x}{(5n) + (6n)x} = \frac{n(3 + 4x)}{n(5 + 6x)} = \frac{3 + 4x}{5 + 6x}$
-Dan
Edit: Also, please use parenthesis when necessary. What you wrote was
$\displaystyle \text{a +b x / c+d x} = a + \frac{bx}{c} + dx$
which is not what you wanted to say. You needed to write this as
(a + b x)/(c + d x)