# Thread: Comparing equations with denominators

1. ## Comparing equations with denominators

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?

2. ## Re: Comparing equations with denominators

I am not sure as to what are you trying to do. I can also say that by having a = 6, b= 8, c =10 and d = 12 the equation is still satisfied. so pl tell us what exactly do you want to do or find out.

3. ## Re: Comparing equations with denominators

if this equation is always true are those the only solutions?
if yes is there any proof of that?

4. ## Re: Comparing equations with denominators

Originally Posted by AaPa
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?
yes

5. ## Re: Comparing equations with denominators

Originally Posted by AaPa
if this equation is always true are those the only solutions?
if yes is there any proof of that?
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.=:
$\frac{(3n) + (4n)x}{(5n) + (6n)x} = \frac{n(3 + 4x)}{n(5 + 6x)} = \frac{3 + 4x}{5 + 6x}$

-Dan

Edit: Also, please use parenthesis when necessary. What you wrote was
$\text{a +b x / c+d x} = a + \frac{bx}{c} + dx$
which is not what you wanted to say. You needed to write this as
(a + b x)/(c + d x)

thanks