Question

plz help...... .....​

Answer 1

$\star\sf\underline\blue{Explanation:-}$

$\sf {(x + y)^{-1} = \bigg(\dfrac{1}{3} + \dfrac{-2}{7} \bigg)^{-1}}$

$\longrightarrow \sf{\bigg[\dfrac{7 + (-6)}{21} \bigg]^{-1}}$

$\longrightarrow \sf{\bigg[\dfrac{7 - 6}{21} \bigg]^{-1}}$

$\longrightarrow \sf{\bigg[\dfrac{1}{21} \bigg]^{-1}}$

$\longrightarrow \boxed{\sf{\purple{21}}}$

$\sf\underline{\green{\:\:\: Now,\:\:\:}}$

$\sf {x^{-1} + y^{-1} = \bigg(\dfrac{1}{3}\bigg)^{-1} + \bigg(\dfrac{-2}{7}\bigg)^{-1}}$

$\longrightarrow \sf {3 + \dfrac{7}{-2}}$

$\longrightarrow \sf {\dfrac{3}{1} + \dfrac{-7}{2}}$

$\longrightarrow \sf {\dfrac{6 - 7}{2}}$

$\longrightarrow \boxed{\sf{\purple{\dfrac{-1}{2}}}}$

$\sf\underline{\pink{\:\:\: Hence,\:\:\:}}$

$\:\:\:\:\dag\bf{\underline{\underline \orange{(x + y)^{-1} \: \neq \: x^{-1} \:+\: y^{-1}}}}$

Answer 2

Answer:

$(x+y)−1=(31+7−2)−1</p><p></p><p>\begin{gathered}\longrightarrow \sf{\bigg[\dfrac{7 + (-6)}{21} \bigg]^{-1}} \\\\ \end{gathered}⟶[217+(−6)]−1</p><p></p><p>\begin{gathered}\longrightarrow \sf{\bigg[\dfrac{7 - 6}{21} \bigg]^{-1}} \\\\ \end{gathered}⟶[217−6]−1</p><p></p><p>\begin{gathered}\longrightarrow \sf{\bigg[\dfrac{1}{21} \bigg]^{-1}} \\\\ \end{gathered}⟶[211]−1</p><p></p><p>\begin{gathered}\longrightarrow \boxed{\sf{\purple{21}}} \\\\\end{gathered}⟶21</p><p></p><p>\sf\underline{\green{\:\:\: Now,\:\:\:}}Now,</p><p></p><p>\begin{gathered}\sf {x^{-1} + y^{-1} = \bigg(\dfrac{1}{3}\bigg)^{-1} + \bigg(\dfrac{-2}{7}\bigg)^{-1}} \\\\ \end{gathered}x−1+y−1=(31)−1+(7−2)−1</p><p></p><p>\begin{gathered}\longrightarrow \sf {3 + \dfrac{7}{-2}}\\\\ \end{gathered}⟶3+−27</p><p></p><p>\begin{gathered}\longrightarrow \sf {\dfrac{3}{1} + \dfrac{-7}{2}}\\\\ \end{gathered}⟶13+2−7</p><p></p><p>\begin{gathered}\longrightarrow \sf {\dfrac{6 - 7}{2}}\\\\ \end{gathered}⟶26−7</p><p></p><p>\begin{gathered}\longrightarrow \boxed{\sf{\purple{\dfrac{-1}{2}}}} \\\\\end{gathered}⟶2−1</p><p></p><p>\sf\underline{\pink{\:\:\: Hence,\:\:\:}}Hence,</p><p></p><p>\:\:\:\:\dag\bf{\underline{\underline \orange{(x + y)^{-1} \: \neq \: x^{-1} \:+\: y^{-1}}}}†(x+y)−1=x−1+y−1</p><p></p><p>$

Step-by-step explanation:

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