[tex]\bf \qquad \qquad \textit{double proportional variation}
\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \textit{\underline{y} varies directly as (x+3) and inversely as (x-3)}\implies y=\cfrac{k(x+3)}{x-3}
\\\\\\
\textit{we also know that }
\begin{cases}
y=21\\
x=4
\end{cases}\implies 21=\cfrac{k(4+3)}{4-3}\implies 21=\cfrac{k(7)}{1}
\\\\\\
\cfrac{21}{7}=k\implies 3=k\qquad thus\qquad \qquad \boxed{y=\cfrac{3(x+3)}{x-3}}[/tex]
