SOLUTION: If m : n is the duplicate ratio of m + x : n + X show that: x^2 = mn. Unable to solve please help

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Question 1086608: If m : n is the duplicate ratio of m + x : n + X show that: x^2 = mn.
Unable to solve please help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Using the definition of Duplicate Ratio, we can say that m/n is equal to the square of (m+x)/(n+x). In other words

m/n = ((m+x)/(n+x))^2

Let's isolate the term x^2 to get...

m/n = ((m+x)/(n+x))^2
m/n = ((m+x)^2)/((n+x)^2)
m(n+x)^2 = n(m+x)^2
m(n^2+nx+x^2) = n(m^2+mx+x^2)
mn^2+mnx+mx^2 = nm^2+mnx+nx^2
mn^2+mx^2 = nm^2+nx^2
mx^2-nx^2 = nm^2-mn^2
(m-n)x^2 = nm^2-mn^2
x^2 = (nm^2-mn^2)/(m-n)
x^2 = (mn(m-n))/(m-n)
x^2 = mn