Question

(x + 1/x) (x - 1/x)​

Answer 1

$\implies \:( x + \dfrac{1}{x} )( x - \dfrac{1}{x} )$

we know that :-

(a+b)(a-b) = a²-b²

$\implies \:( x + \dfrac{1}{x} )( x - \dfrac{1}{x} ) = {(x)}^{2} - { (\dfrac{1}{x}) }^{2}$

$\implies \:( x + \dfrac{1}{x} )( x - \dfrac{1}{x} ) = {x}^{2} - { \dfrac{1}{ {x}^{2} }}$

Answer :

${x}^{2} - { \dfrac{1}{ {x}^{2} }}$

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$\implies{(a+b)^2 = a^2 + b^2 + 2ab}$

$\implies{(a-b)^2 = a^2 + b^2 - 2ab}$

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

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$1)a^m \times a^n= {a}^{(m + n)}$

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

$3) {ab}^{n} = {a}^{n} {b}^{n}$

$4) \frac{ {(a)}^{m} }{ {(a)}^{n} } = {a}^{m - n}$

$5) {a}^{ - b} = \frac{1}{ {a}^{b} }$

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