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Identities of Mathematical Operations

given x+y+z *...

Question

given (x+y+z)*(ab+1)=1 find the value of z if x is additive inverse of y and a is multiplactive inverse of b.

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Solution

Additive inverse of a number is negative of that number.
Multiplicative inverse of a number is it's reciprocal.

(x+y+z)(ab+1)=1
y=-x
b=1/a
So,
(x+(-x)+z)(a(1/a)+1)=1
z2 =1
z=1/2

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