[tex] {(m + n)}^{ - 1} ( {m}^{ - 1} + {n}^{ - 1} )[/tex]
[tex] = (\frac{1}{m + n})( \frac{1}{m} + \frac{1}{n} )[/tex]
[tex] = (\frac{1}{m + n} )( \frac{m + n}{mn} )[/tex]
[tex] = \frac{1}{mn} [/tex]
[tex] = {(mn)}^{ - 1} [/tex]
(m+n)^-1 (m^-1 + n^-1) = (mn)^-1
1/m+n × 1/m + 1/m = 1/mn
1/m+n × n/mn + m/mn = 1/mn
1/m+n × n+m/nm = 1/mn
1/m+n × m+n/nm = 1/mn
1 × m+n / m+n×nm = 1/mn
m+n cancel out, gives
1/mn = 1/mn
Lhs = Rhs
Hence Proved
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Verified answer
[tex] {(m + n)}^{ - 1} ( {m}^{ - 1} + {n}^{ - 1} )[/tex]
[tex] = (\frac{1}{m + n})( \frac{1}{m} + \frac{1}{n} )[/tex]
[tex] = (\frac{1}{m + n} )( \frac{m + n}{mn} )[/tex]
[tex] = \frac{1}{mn} [/tex]
[tex] = {(mn)}^{ - 1} [/tex]
(m+n)^-1 (m^-1 + n^-1) = (mn)^-1
1/m+n × 1/m + 1/m = 1/mn
1/m+n × n/mn + m/mn = 1/mn
1/m+n × n+m/nm = 1/mn
1/m+n × m+n/nm = 1/mn
1 × m+n / m+n×nm = 1/mn
m+n cancel out, gives
1/mn = 1/mn
Lhs = Rhs
Hence Proved