Comparing equations with denominators

• October 24th 2013, 09:10 PM
AaPa
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?
• October 24th 2013, 09:20 PM
ibdutt
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.
• October 24th 2013, 10:08 PM
AaPa
Re: Comparing equations with denominators
if this equation is always true are those the only solutions?
if yes is there any proof of that?
• October 25th 2013, 04:40 AM
votan
Re: Comparing equations with denominators
Quote:

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
• October 25th 2013, 04:54 AM
topsquark
Re: Comparing equations with denominators
Quote:

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)
• October 30th 2013, 10:10 AM
AaPa
Re: Comparing equations with denominators
thanks