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Question
5m - n = 3m + 4n then find the value of the following expression.
`["m"^2 + "n"^2]/["m"^2 - "n"^2]`
Solution
5m - n = 3m + 4n
⇒ 5m - 3m = n + 4n
⇒ 2m = 5n
⇒ `m/n = 5/2`
`therefore [m^2 + n^2]/[m^2 - n^2]`
Dividing by `n^2`
= `[m^2/n^2 + n^2/n^2]/[m^2/n^2 - n^2/n^2`
= `[25/4 + 1]/[25/4 - 1]` ...`(m/n = 5/2)`
= `29/21`
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