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?

Printable View

- Oct 24th 2013, 09:10 PMAaPaComparing 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? - Oct 24th 2013, 09:20 PMibduttRe: 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.

- Oct 24th 2013, 10:08 PMAaPaRe: Comparing equations with denominators
if this equation is always true are those the only solutions?

if yes is there any proof of that? - Oct 25th 2013, 04:40 AMvotanRe: Comparing equations with denominators
- Oct 25th 2013, 04:54 AMtopsquarkRe: Comparing equations with denominators
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) - Oct 30th 2013, 10:10 AMAaPaRe: Comparing equations with denominators
thanks