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here is ur answer
Step-by-step explanation:
Correction in Question : other wise LHS = 2
(x⁻¹ + y⁻¹)/x⁻¹ + (x⁻¹ - y⁻¹)/y⁻¹ = (x² + y²)/xy
LHS
= (x⁻¹ + y⁻¹)/x⁻¹ + (x⁻¹ - y⁻¹)/y⁻¹
= (1/x + 1/y)/(1/x) + (1/x - 1/y)/(1/y)
= x(y + x) /xy + y(y - x)/xy
= (1/xy) ( xy + x² + y² - yx)
= (1/xy) ( x² + y²)
= (x² + y²)/xy
= RHS
QED
Hence Proved
(x⁻¹ + y⁻¹)/x⁻¹ + (x⁻¹ - y⁻¹)/y⁻¹ = (x² + y²)/xy
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