Question 221499: 1/s+a + 1/s+b = 1/c solve for s
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 1/(s+a) + 1/(s+b) = 1/c
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LCD = (s+a)(s+b)(c),,,,,multiply thru by LCD
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c(s+b) + c(s+a) = (s+a)(s+b) ,,,,,,,expand and simplify
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cs +cb +cs+ ca = s^2 +sb +sa +ab
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s^2 +sa +sb -2cs = ca -ab +cb
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s^2 +s(a+b -2c) +( ab -ca-cb) =0
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using quadratic formula
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(a=(1),,,,b=(a+b-2c),,,,c=(ab-ca-cb)
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s= [-(a+b-2c) +/- sqrt{ (a+b-2c)^2 -4(1)(ab-ca-cb)}] / 2(1)
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s= [2c-a-b +/- sqrt{ (a+b)^2 -4(a+b)c +4c^2 -4ab +4ac +4bc} ] / 2
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s= [2c -a-b +/- sqrt { (a+b)^2 -4c^2 -4ac-4bc -4ab +4ac +4bc}]/2
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s= [2c-a-b +/- sqrt{ (a+b)^2 -4c^2 -4ab)}]/2
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s= [ 2c-a-b +/- sqrt{ ((a+b) +2c)( (a+b) -2c)}]/2
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s= [ -( (a+b) -2c) +/- sqrt { ( (a+b) +2c)( (a+b) -2c)}]/2
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Hopefully this is close to the answer
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Please check the math one more time. A goal would be to get sqrt{ x-y}^2,,,but it is what it is.
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