Login

show that x^-1 + y^-1 / x^-1 +x^-1 - y^-1 / y^-1=x²+y²/xy

$L H S, \frac{x^{- 1} + y^{- 1}}{x^{- 1}} + \frac{x^{- 1} - y^{- 1}}{y^{- 1}} = \frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x}} + \frac{\frac{1}{x} - \frac{1}{y}}{\frac{1}{y}} = \frac{\frac{x + y}{x y}}{\frac{1}{x}} + \frac{\frac{y - x}{x y}}{\frac{1}{y}} = \frac{x + y}{x y} * \frac{x}{1} + \frac{y - x}{x y} * \frac{y}{1} = \frac{x + y}{y} + \frac{y - x}{x} = \frac{x (x + y) + y (y - x)}{x y} = \frac{x^{2} + x y + y^{2} - y x}{x y} = \frac{x^{2} + y^{2}}{x y} = R H S H e n c e p r o v e d .$

30

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?