Hello and thank you for your help! I don't understand the answer provided by my book.
An operation θ is defined by the equation a θ b = a-b/a+b, for all numbers a and b such that a does not equal -b. If a does not equal -c and a θ c = 0, then c = ?
The correct answer is that c = a
Substitute c for b and 0 for a θ c in the given equation and solve for c.
So 0 = a - c / a + c
Multiply each side by a + c
So 0 = a - c
So c = a
My question is: why can they substitute c for b?
Source: 12th edition Gmat Review
θ has been defined as an operator which takes input values of two variables and gives the answer by calculating (First variable - Second variable)/(First variable + Second variable). Here a and b are just taken as an example.
a θ b = (a - b)/(a + b)
x θ y = (x - y)/(x + y)
a θ c = (a - c)/(a + c)
It doesn't what the two variables are.
Given a θ c = 0 = (a - c)/(a + c)
Then a - c = 0
a = c
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