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Question
If `(m + n)/(m + 3n) = 2/3`, find : `(2n^2)/(3m^2 + mn)`.
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Solution
Given: `(m + n)/(m + 3n) = 2/3`
`\implies` 3m + 3n = 2m + 6n
`\implies` 3m – 2m = 6n – 3n
`\implies` m = 3n
Now `(2n^2)/(3m^2 + mn)`
= `(2n^2)/(3(3n)^2 + 3n xx n)`
= `(2n^2)/(27n^2 + 3n^2)`
= `(2n^2)/(30n^2)`
= `1/15`
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