Fer the luvva god, help me do complex fractions

Factual Questions
1

Who knew I’d need to remember this crap from 25 years ago…

I’m trying to simplify a formula. Said formula looks like:

(((x^-.696) x 0.3494)/(0.3494^-.696))-.3494

Now, my x in my test case is 0.2613. Working out the equation, my result should be .0783.

I’ve simplified to here (thanks Wolfram|Alpha):

(.3494/((x^.696)/(.481008)))-.3494

Does it get any simpler? Can I do the whole flippy thing to the bottom fraction and get it into a single fraction? I can’t get any simpler fraction to return the correct result, but it looks like it should be simplifierable. This thing is really starting to piss me off.

2

Symbolic notation is your friend. The formula you’ve got there is really nothing more than

a/(b/c) - a,

where a = .3494, b = .2613^.696, and c = .481008.

The formula easily simplifies to a(c/b) - a or a(c/b - 1).

So you just compute (.3494)(.481008/(.2613^.696) - 1), and voila, you get 0.0783068.

3

Work it through.

Let a = 0.696, b = 0.3494.

So you have (x[sup]-a[/sup]b / b[sup]-a[/sup]) - b

Which you can simplify to (b[sup]a+1[/sup] / x[sup]a[/sup]) -b

Or b((b[sup]a[/sup] / x[sup]a[/sup]) - 1)
Now plug in your values.

4

How the heck did you get that? Where’d all the exponents go?

5

Kimstu plugged in the specific value of 0.2613 as X. You’ll see that the exponent is there in her definition of b.

Can I ask the OP what they’re doing that has so many 0.3494s involved? You can “do the whole flippy thing to the bottom fraction”, yeah, to turn it into (0.3494 * 0.481008) / (X^0.696) - 0.3494. But I’m curious where this comes from.

6

Yeah, I reduced the OP’s second (simplified) version of the expression, sorry if it was confusing.

7

Thanks for the help! I just knew it could get simpler!

x is the decimal value of the degree that industrial buildings cover the land on the basis of total building area over lot area. The median coverage of the properties that we have examined is 34.94%. This data is being used in a multiple regression model to estimate the value of industrial properties in the city in order to try to generate a reduction in the assessed value (and thus, their tax).