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May 22nd, 2015, 12:21 PM   #1
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Need to solve for α

Hello, I'm new here. It was good to find about this forum. Interested in exchanging ideas, even though I'm no math wizard.

Anyway, my current problem is that I need to solve the following equation for α:

p(f − 1)/(1 − α + fα) − (1 − p)/(1 − α) = 0

I already know the answer, which is α = (pf − 1)/(f-1), but I can't solve it by myself. I've tried a few different ways but can't figure out what are the steps to get to the solution.

I'd be really glad if someone could help me out with this. Thanks in advance
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May 22nd, 2015, 02:12 PM   #2
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p(f − 1)/(1 − α + fα) − (1 − p)/(1 − α) = 0 (I'll assume f = 1 and p = 1 are not true.)
Multiply through by (1 − α + fα)(1 − α):
p(f − 1)(1 − α) − (1 − p)(1 − α + fα) = 0
Hence p(f - 1) - pα(f - 1) - (1 − p) + α(1 − p) - fα(1 − p) = 0,
and so pα(f - 1) - α(1 − p) + fα(1 − p) = p(f - 1) - (1 − p) = pf - 1.
Hence α = (pf - 1)/(p(f - 1) - (1 − p) + f(1 − p)) = (pf - 1)/(pf - p - 1 + p + f − fp) = (pf - 1)/(f - 1).

If p = 1 or f = 1, they must both equal 1 and α can have any value except 1.
Thanks from MRebel
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May 22nd, 2015, 02:55 PM   #3
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Nice! Thanks
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May 22nd, 2015, 06:47 PM   #4
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Quote:
Originally Posted by MRebel View Post
p(f − 1)/(1 − α + fα) − (1 − p)/(1 − α) = 0
Another way; rearrange:
p(f − 1)/(1 − α + fα) = (1 − p)/(1 − α)
Crisscross multiplication:
1 - a + fa - p + pa - fpa = pf - p - fpa + pa
Simplify:
1 - a + fa = pf
Rearrange:
fa - a = pf - 1
wrap-up:
a(f - 1) = pf - 1
a = (pf - 1) / (f - 1)
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