Question

8. Prove that :
(1) (x + y)-'(x-' + y - 1) =
1
ху​

Answer 1

Answer:

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Step-by-step explanation:

Given : (x⁻¹  + y⁻¹)/x⁻¹    + (x⁻¹  - y⁻¹)/y⁻¹  = (x² + y²)/xy

To find : Prove the equality

Solution:

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

Answer 2

Answer:

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Step-by-step explanation:

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