- #1

karush

Gold Member

MHB

- 3,269

- 5

The reciprocal of half a number increased by half the recipical of the number is $\dfrac{1}{2}$

$\begin{array}{rl}

n= & \textit{the number} \\ \\

\dfrac{n}{2}= &\textit{half the number}\\ \\

\dfrac{2}{n} = &\textit{the reciprocal of half the number}\\ \\

\dfrac{1}{2n}= & \textit{half the reciprocal of the number}\\ \\

\dfrac{2}{n}+\dfrac{1}{2n} &=\dfrac{1}{2}\\ \\

&\textit{Multiply every term by 6n to cancel denominators}\\ \\

12+3=15 &=3n\quad\therefore n=5

\end{array}$

hopefully :unsure: