Question : If $a+b=2c$, then find $\frac{a}{a–c}+\frac{c}{b–c}$:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Answer (1)
19th Jan, 2024
Correct Answer: 1
Solution :
Given: $a+b=2c$
⇒ $a-c=c-b$
Putting this value in the expression $\frac{a}{a–c}+\frac{c}{b–c}$, we have,
$=\frac{a}{a–c}+\frac{c}{b–c}$
$=\frac{a}{a–c}-\frac{c}{a–c}$ $[\because b-c=–(a-c)]$
$=\frac{a–c}{a–c}=1$
Hence, the correct answer is 1.
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