SOLUTION: If x = (ab)/(a+b), hence prove sqrt[(a-x)/(b-x)] = a/b.

Question 1121756: If x = (ab)/(a+b), hence prove sqrt[(a-x)/(b-x)] = a/b.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
see my worksheet below.

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step 1 shows the given relationship.

step 2 replaces x in (a-x) with ab/(a+b) and solves to get (a-x) = a^2/(a+b).

step 2 replaces x in (b-x) with ab/(a+b) and solve to get (b-x) = b^2/(a+b).

step 3 replaces (a-x) with a^2/(a+b) and replaces (b-x) with b^2/(a+b) and solves for (a-x)/(b-x) in terms of a and b equivalents to get (a-x)/(b-x) = a^2/b^2.

step 4 takes the square root of (a^2/b^2) to get a/b.

step 5 confirms that this proves that sqrt((a-x)/(b-x)) is equal to a/b.

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