Question

14. Show that :- x-¹+y-¹/x-¹ + x-¹-y-¹/x-¹ = x²+y²/xy.

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Answer 1

$\huge\color{blue}\boxed{\colorbox{black}{Answer : ♞ }}$

$= > \: \frac{ {x}^{ - 1} + {y}^{ - 1} }{ {x}^{ - 1} } + \frac{ {x}^{ - 1} - {y}^{ - 1} }{ {y}^{ - 1} }$

$= > \: \frac{ \frac{1}{x} + \frac{1}{y} }{ \frac{1}{x} } + \frac{ \frac{1}{x} - \frac{1}{y} }{ \frac{1}{y} }$

$= > \: \frac{x + y}{xy} \times x \: + \frac{y - x}{xy} \times y$

$= > \: \frac{x + y}{y} + \frac{ y- x}{x}$

$= > \: \frac{x(x + y) + y(y - x)}{xy}$

$= > \: \frac{ {x}^{2} +xy + {y}^{2} - xy }{xy}$

$= > \: \frac{ {x}^{2} + {y}^{2} }{xy}$

$= > \: \color {green}RHS$

$</p><p>\huge\color{red}\boxed{\colorbox{yellow}{Hence proved }}$

Answer 2

$\large \sf \green{HOPE} \: \pink{THIS} \: \blue{IS \: HELPFUL} \: \red{FOR \: YOU}$