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January 3rd, 2017, 02:04 PM  #1 
Newbie Joined: Jan 2017 From: uk Posts: 1 Thanks: 0  inverting an equation
Hi, I have this equation that I need to invert: (a * b) / (a + b) = c. I want to use a value in c, say 100, and have a value in a, say 10, to find out the answer to b, instead. Last edited by skipjack; January 3rd, 2017 at 03:19 PM. 
January 3rd, 2017, 02:10 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 753 Thanks: 399 
$\dfrac{a b}{a+b}=c$ $a b = c(a+b)$ $a b  c b = c a$ $b(a  c) = c a$ if $a \neq c$ $b = \dfrac{a c}{a  c}$ if $a = c$ then $b(0) = c^2$ $0 = c^2$ $c = a = 0$ and $b$ can be any value at all. so $b = \begin{cases} \dfrac{a c}{a  c} & a \neq c \\ \\ x \in \mathbb{R} &a=c \end{cases}$ 
January 3rd, 2017, 02:12 PM  #3 
Newbie Joined: Nov 2016 From: Canada Posts: 13 Thanks: 3 Math Focus: All 
(10*b) = 100 *(10+b) 10b = 100(10+b) b = 10(10+b) b = 100 +10b 9b = 100 b = 100/9 
January 4th, 2017, 03:06 AM  #4 
Member Joined: Sep 2016 From: kota Posts: 63 Thanks: 14 
$\dfrac{a×b}{a+b}=c$ Put values $\dfrac{10×b}{10+b}=100$ multiply both sides by $(10+b)$ $10b=100(10+b)$ $10b=1000+100b)$ $10b1000b= 1000$ $90b=1000$ $b=\dfrac{1000}{90b}$ $b=\dfrac{100}{9}$ 
January 4th, 2017, 09:32 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,144 Thanks: 552  

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