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If $\frac{1}{x+2}, \frac{1}{x+3}, \frac{1}{x+5}$ are in A.P. then x = ?

A. 5 B. 3 C. 1 D. 2 Answer: Option C
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Solution(By Apex Team)

$\begin{aligned}&\frac{1}{x+2},\frac{1}{x+3},\frac{1}{x+5}\text{ are in A.P. }\\ &\therefore\frac{1}{x+3}-\frac{1}{x+2}=\frac{1}{x+5}-\frac{1}{x+3}\\ &\Rightarrow\frac{x+2-x-3}{(x+3)(x+2)}=\frac{x+3-x-5}{(x+5)(x+3)}\\ &\Rightarrow\frac{-1}{(x+3)(x+2)}=\frac{-2}{(x+5)(x+3)}\\ &\Rightarrow\frac{-1}{x+2}=\frac{-2}{x+5}\\ &\Rightarrow-2x-4=-x-5\\ &\Rightarrow-2x+x=-5+4\\ &\Rightarrow-x=-1\\ &\therefore x=1\end{aligned}$

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