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Question
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find `(2m^2 - 11n^2)/(2m^2 + 11n^2)`
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Solution
`m/n = 11/4`
`m^2/n^2 = 121/16`
`(2m^2)/(11n^2) = (2 xx 121)/(11 xx 16)` ...`("Multiplying both sides by" 2/11)`
`(2m^2)/(11n^2) = 11/8`
`(2m^2 + 11n^2)/(2m^2 - 11n^2) = (11 + 8)/(11 - 8)` ...(Applying componendo and divdendo)
`(2m^2 + 11n^2)/(2m^2 - 11n^2) = 19/3`
`(2m^2 - 11n^2)/(2m^2 + 11n^2) = 3/19` ...(Applying invertendo)
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