Question

please answer this question correctly

Answer 1

c) -a/(a+1) .

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Answer 2

Given : a  * b = a + b + ab    on  R - { - 1}

To find : a ⁻¹  

Solution:

a * a ⁻¹  = a⁻¹ * a  = e

a o e  = e o a  = a

a * e  = e  * a

a * e   = a  +  e  +  ae   = a  =   e  +  a  + ea  

=> e (1 + a) = 0  

=> e = 0    or  a  = - 1   but a ≠ - 1 Given

Hence e = 0

a * a ⁻¹  =  e  = a ⁻¹ * a

=> a * a ⁻¹   = 0

=> a  + a ⁻¹  + a a ⁻¹   = 0

=> a +  a ⁻¹  (1 + a) = 0

=>  a ⁻¹  = -a/(1 + a)

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