Question

An operation $\theta$ is defined by the equation
$a\theta b=\frac{a-b}{a+b}$, for all numbers a and b such that $a\ne -b$. If $a\ne -c$ and $a\theta c=0$, then find the value of c.

• A. $-a$
• B. $-\frac{1}{a}$
• C. $0$
• D. $\frac{1}{a}$
• E. $a$

Answer 1

The correct option is E $a$

$\frac{(a-c)}{(a+c)}$ = 0 ----------Given

So, numerator $(a-c)$ must be equal to 0

Thus, a = c OR c = a. (option E)