Question : If $a+b=2c$, then the value of $\frac{a}{a–c}+\frac{c}{b–c}$ is equal to (where $a\neq b\neq c$):
Option 1: $–1$
Option 2: $1$
Option 3: $0$
Option 4: $\frac{1}{2}$
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Correct Answer: $1$
Solution :
Given: $a+b=2c$
⇒ $a-c=c-b$
Now, $\frac{a}{a-c}+\frac{c}{b-c}$ can be written as,
$=\frac{a}{a-c}-\frac{c}{c-b}$
$=\frac{a}{a-c}-\frac{c}{a-c}$
$=\frac{a-c}{a-c}= 1$
Hence, the correct answer is $1$.
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