Question

1/m+1/a=2(1/m-1/n)then m:n​

Answer 1

Step-by-step explanation:

the correct answer is 8:1

Answer 2

Appropriate Question:

$\tt \: \dfrac{1}{m} + \dfrac{1}{n} = 2 \bigg( \dfrac{1}{m} - \dfrac{1}{n} \bigg) \: \: \: then \: \: \: \: m : n$

Solution:

$\: \: \: \: \: \tt \: \dfrac{1}{m} + \dfrac{1}{n} = 2 \bigg( \dfrac{1}{m} - \dfrac{1}{n} \bigg) \: \: \: \\ \\ \\ \tt : \implies \frac{(1 \times n) + (1\times m)}{mn} = 2 \bigg(\frac{(1 \times n) - (1\times m)}{mn} \bigg) \\ \\ \\ \tt \ \: : \implies \frac{n +m }{mn} = 2 \bigg(\frac{n - m}{mn} \bigg) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Canceling (mn) both sides:

$\\ \tt : \implies \frac{n +m }{ \cancel{mn} }= 2 \bigg(\frac{n - m}{ \cancel{mn}} \bigg) \\ \\ \\ : \implies \tt \: n + m = 2(n - m) \\ \\ \\ : \implies\tt \: n + m = 2n - 2m \\ \\ \\ \tt : \implies \: m + 2m = 2n - n \\ \\ \\ \tt : \implies3m = n \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \frac{m}{n} = \frac{1}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \: m : n = 1: 3$

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Hope it helps you! :)