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Question
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
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Solution
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Applying componendo and dividendo,
`(sqrt(x + 5)+ sqrt(x - 16) + sqrt(x + 5) - sqrt(x - 16))/(sqrt(x + 5)+sqrt(x - 16) - sqrt(x + 5) + sqrt(x -16)) = (7 + 3)/(7 - 3)`
`(2sqrt(x + 5))/(2sqrt(x - 16)) = 10/4`
`sqrt(x + 5)/sqrt(x - 16) = 5/2`
Squaring both sides,
`(x + 5)/(x - 16) = 25/4`
4x + 20 = 25x – 400
21x = 420
`x = 420/21 = 20`
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