SOLUTION: If 1/x = 1/a + 1/b , determine the value of x. Hence prove sqrt(a-x/b-x) = a/b

Algebra ->  Equations -> SOLUTION: If 1/x = 1/a + 1/b , determine the value of x. Hence prove sqrt(a-x/b-x) = a/b       Log On


   

Question 1121712: If 1/x = 1/a + 1/b , determine the value of x. Hence prove sqrt(a-x/b-x) = a/b
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1/x = 1/a + 1/b
:
1/x = (b+a)/ab
:
cross multiply fractions
:
x(b+a) = ab
:
************
x = ab/(b+a)
************
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sqrt( (a-x)/(b-x) ) =
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sqrt( (a-(ab/(b+a))/(b-(ab/(b+a)) ) =
:
sqrt( (ab+a^2-ab)/(b+a)/(b^2+ab-ab)/(b+a) ) =
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sqrt( (a^2/(b+a)) / (b^2/(b+a)) ) =
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sqrt( (a^2/(b+a)) * ((b+a)/b^2) ) =
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sqrt( a^2/b^2) =
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a/b or -a/-b = a/b, or -a/b or a/-b
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