I apologize for the somewhat cryptic title as I don't quite know how to word it.
I have a somewhat abstract question that may have a simple answer. But I am wracking my mind all over this!
So assume I have three variables X, Y, and Z
So say I have variable Z which is the number X divided by the sum of X and Y, something mathematically written as Z = X / (X + Y), so X and Y are weighted in determining Z.
Is there a way I can keep this relationship but remove the effects of the Y variable?
So for example, say X = 2, Y = 2, so Z = 2/(2+2) = 2 in on instance
In the second instance X = 2, but Y = 4 so Z = 2/(2+4) = 4 so the value of Z naturally changes because Y is a larger number. Is there a way I could add/adjust this formula so that even though Y is a larger number (in this case 4), I can make Z = 2 again?
Practically speaking, I want to determine how to adjust a equation for changes in one of it's variables to remove the effect of a change in the value (but still maintain the weighting).
Is this even possible? I have to admit my knowledge of mathematics is slight!
First off, don't forget your order of operations! $\ x=2 $ and $\ y=2 $ gives the equation $$z = 2 / (2 + 2) $$ $$z = 2 / 4 $$ $$z = 1 / 2 $$
In general, fix $\ z $ to be some constant number $\ c $. $\ c $ can be any number you like: 2, -13, 965, etc.
$$ z = c $$
Then because $\ z = x / (x + y) $, it is easy to rearrange the variables to have it in the form y = (some function of x)
$$ c = x / (x+y) $$ $$ c(x+y) = x $$ $$ cx + cy = x $$ $$ cy = x - cx $$ $$ y = (x- cx) / c $$ $$ y = (x/c) - x $$
So in the case of $\ z = 2 $, $$ y = (x/2) - x = -(x/2) $$ where x is any real number.For example, let x = 5. then y= -(5/2) gives the equation $$z = 5 / (5 -(5/2)) $$ $$z = 5 / ((10/2) - (5/2)) $$ $$ z = 5 / (5/2) $$ $$ z = 2 $$
Hope that helps.