Question

7m+2n/7m-2n=5/3, find (m^2+n^:m^2-n^2)

Answer 1

$\frac{7m + 2n}{7m - 2n} = \frac{5}{3} \\ 21m + 6n = 35m - 10n \\ 6n + 10n = 35m - 21m \\ 16n = 14m \\ 8n = 7m \\ n = \frac{7}{8}m \\ {n}^{2} = \frac{49}{64} {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i) \\ \\ \: \: \: \: \: \frac{ {m}^{2} + {n}^{2} }{ {m}^{2} - {n}^{2} } \\ = \frac{ {m}^{2} + \frac{49}{64} {m}^{2} }{ {m}^{2} - \frac{49}{64} {m}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: from (i) \\ \\multiplying \: numerator \: and \: denominator \: by \:\\ 64\\ \\ = \frac{64 {m}^{2} + 49 {m}^{2} }{64 {m}^{2} - 49 {m}^{2} } = \frac{113 {m}^{2} }{15 {m}^{2} } \\ = \frac{113}{15}$

Hence,

(m² + n²):(m² - n²) = 113:15

Answer 2

*CHECK HERE*

IT WILL BE HELPFUL

Answer:

1) 8:7

2) 113: 15

Step-by-step explanation: