Question

show that {( x-¹+y-¹/x-¹) + (x-¹-y-¹/x-¹)} = x²+y²/xy​

Answer 1

Step-by-step explanation:

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Answer 2

$\Huge\bf\maltese{\underline{\green{Answer°᭄}}}\maltese$

$\implies$$\large\bf{\underline{\red{VERIFIED✔}}}$

$LHS, \\ = > \frac{{x}^{ - 1} + {y}^{ - 1} }{ {x}^{ - 1} } + \frac{{x}^{ - 1} - {y}^{ - 1} }{ {y}^{ - 1} } \\ \\ = > \frac{ \frac{1}{x} + \frac{1}{y} }{ \frac{1}{x} } + \frac{ \frac{1}{x} - \frac{1}{y} }{ \frac{1}{y} } \\ \\ = > \frac{ \frac{x + y}{xy} }{ \frac{1}{x} } + \frac{ \frac{y - x}{xy} }{ \frac{1}{y} } \\ \\ = > \frac{x + y}{xy } \times \frac{x}{1} + \frac{y - x}{xy} \times \frac{y}{1} \\ \\ = > \frac{x + y}{y} + \frac{y - x}{x} \\ \\ = > \frac{x(x + y) + y(y - x)}{xy} \\ \\ = > \frac{ {x}^{2 } + xy + {y}^{2} - yx}{xy} \\ \\ = > \frac{ {x}^{2} + {y}^{2} }{xy} \\ \\ = > RHS.$

$\boxed{I \:Hope\: it's \:Helpful}$