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May 22nd, 2015, 12:21 PM  #1 
Newbie Joined: May 2015 From: Brazil Posts: 2 Thanks: 0  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)/(f1), 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 
May 22nd, 2015, 02:12 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,464 Thanks: 2038 
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. 
May 22nd, 2015, 02:55 PM  #3 
Newbie Joined: May 2015 From: Brazil Posts: 2 Thanks: 0 
Nice! Thanks

May 22nd, 2015, 06:47 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,274 Thanks: 1023  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 wrapup: a(f  1) = pf  1 a = (pf  1) / (f  1) 

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