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 CShow Answer
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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