If m - - n then m - n -1- m -1- n -1-A- 0B- mnC- m -1 n -1D- m -2 n -2

The correct option is C m^ 1n^ 1 Given (m + n)^ 1 × (m^ 1 + n^ 1), ⇒ 1/m +n × (1/m + 1/n) (∵ a^ m = 1/a^m) ⇒ 1/m +n × (m + n/nm) ⇒ m + n/(m ...

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Byju's Answer

Standard VII

Mathematics

a^m x b^m = (ab)^m

If m / = n th...

Question

If $m \neq n$ then $(m + n)^{- 1} \times (m^{- 1} + n^{- 1}) =$ ______

$m n$

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$m^{- 1} n^{- 1}$

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$m^{- 2} n^{- 2}$

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Solution

The correct option is C
$m^{- 1} n^{- 1}$

Given

$(m + n)^{- 1} \times (m^{- 1} + n^{- 1})$ ,

$\Rightarrow \frac{1}{m + n} \times (\frac{1}{m} + \frac{1}{n})$ ( $∵ a^{- m} = \frac{1}{a^{m}}$ )

$\Rightarrow \frac{1}{m + n} \times (\frac{m + n}{n m})$

$\Rightarrow \frac{m + n}{(m + n) m n}$ = $\frac{1}{m n} = (m n)^{- 1}$

$\Rightarrow (m n)^{- 1} = m^{- 1} n^{- 1}$ ( $∵ (a b)^{m} = a^{m} \times b^{m}$ )

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If m≠n then (m+n)−1 × (m−1 + n−1) = ______

The correct option is C m−1n−1 Given (m+n)−1 × (m−1 + n−1), ⇒ 1m+n × (1m+1n) (∵a−m = 1am) ⇒ 1m+n × (m+nnm) ⇒ m+n(m+n)mn = 1mn = (mn)−1 ⇒ (mn)−1 = m−1n−1 (∵(ab)m = am×bm)

If $m \neq n$ then $(m + n)^{- 1} \times (m^{- 1} + n^{- 1}) =$ ______