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Solve the equation
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$x \div y = \dfrac { y } { x }$
$x \div y = \dfrac{ y }{ x }$
$\begin{cases} x ^ { 2 } = y ^ { 2 } \\ y \neq 0 \\ x \neq 0 \end{cases}$
Solve the fractional equation
$\color{#FF6800}{ x } \color{#FF6800}{ \div } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { y } { x } }$
 Reverse the left and right terms of the equation (or inequality) 
$\color{#FF6800}{ \dfrac { y } { x } } = \color{#FF6800}{ x } \color{#FF6800}{ \div } \color{#FF6800}{ y }$
$\color{#FF6800}{ \dfrac { y } { x } } = \color{#FF6800}{ x } \color{#FF6800}{ \div } \color{#FF6800}{ y }$
 If $\frac{a(x)}{b(x)} = c(x)$ is valid, it is $\begin{cases} a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ x } \left ( \color{#FF6800}{ x } \color{#FF6800}{ \div } \color{#FF6800}{ y } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ x } \left ( \color{#FF6800}{ x } \color{#FF6800}{ \div } \color{#FF6800}{ y } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Simplify the expression 
$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { x ^ { 2 } } { y } } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { x ^ { 2 } } { y } } \\ x \neq 0 \end{cases}$
 Reverse the left and right terms of the equation (or inequality) 
$\begin{cases} \color{#FF6800}{ \dfrac { x ^ { 2 } } { y } } = \color{#FF6800}{ y } \\ x \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ \dfrac { x ^ { 2 } } { y } } = \color{#FF6800}{ y } \\ x \neq 0 \end{cases}$
 If $\frac{a(x)}{b(x)} = c(x)$ is valid, it is $\begin{cases} a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ y } \color{#FF6800}{ y } \\ \color{#FF6800}{ y } \neq \color{#FF6800}{ 0 } \end{cases} \\ x \neq 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ y } \color{#FF6800}{ y } \\ \color{#FF6800}{ y } \neq \color{#FF6800}{ 0 } \end{cases} \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 If there is a system of equations (inequality) in the system of equations (inequality), take it out. 
$\begin{cases} \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ y } \color{#FF6800}{ y } \\ \color{#FF6800}{ y } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ y } \color{#FF6800}{ y } \\ \color{#FF6800}{ y } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Simplify the expression 
$\begin{cases} \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \\ \color{#FF6800}{ y } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
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