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
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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Question : If $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}$, then $(x+y+z)$ is:
Question : The numerical value of $\frac{(a–b)^{2}}{(b–c)(c–a)}+\frac{(b–c)^{2}}{(c–a)(a–b)}+\frac{(c–a)^{2}}{(a–b)(b–c)}$ is: $(a\neq b\neq c)$
Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.
Question : If $a+b+c=0$, then the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}$ is:
Question : If $(a^2 = b + c)$, $(b^2 = a + c)$, $(c^2 = b + a)$. Then, what will be the value of $(\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1})$?
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