Given:(x+y+z)×(ab+1)=1

Find the value of z if x is additive inverse of y and a is multiplicative inverse of b.

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Solution

(x+y+z)×(ab+1)=1
Given
x is additive inverse of y
that is x=-y.............(1)
a is multiplicative inverse of b.
that is a=1/b............(2)
So (x+y+z)×(ab+1)=1
From (1) and (2)
=(-y+y+z)((1/b)b+1)=1
=z(1+1)=1
z*2=1
z=1/2

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