Solve for: (4)/(x)=(x)/(9)

Expression: $\frac{ 4 }{ x }=\frac{ x }{ 9 }$

Determine the defined range

$\begin{array} { l }\frac{ 4 }{ x }=\frac{ x }{ 9 },& x≠0\end{array}$

Simplify the equation using cross-multiplication


Swap the sides of the equation


Take the square root of both sides of the equation and remember to use both positive and negative roots


Write the solutions, one with a $+$ sign and one with a $-$ sign

$\begin{array} { l }\begin{array} { l }x=-6,\\x=6\end{array},& x≠0\end{array}$

Check if the solution is in the defined range

$\begin{array} { l }x=-6,\\x=6\end{array}$

The equation has $2$ solutions

$\begin{array} { l }x_1=-6,& x_2=6\end{array}$