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Formula
Solve the equation
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$y = \dfrac { 11 } { x } - 2$
$y = \dfrac { 3 } { x }$
Asymptote
$y = - 2$, $x = 0$
Standard form
$y = \dfrac { 11 } { x } - 2$
Domain
$y \neq - 2$
Range
$x \neq 0$
$x$Intercept
$\left ( \dfrac { 11 } { 2 } , 0 \right )$
Asymptote
$y = 0$, $x = 0$
Standard form
$y = \dfrac { 3 } { x }$
Domain
$y \neq 0$
Range
$x \neq 0$
$\dfrac{ 11 }{ x } -2 = \dfrac{ 3 }{ x }$
$x = 4$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { 11 } { x } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \color{#FF6800}{ \dfrac { 3 } { x } }$
 Reverse the left and right terms of the equation (or inequality) 
$\color{#FF6800}{ \dfrac { 3 } { x } } = \color{#FF6800}{ \dfrac { 11 } { x } } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ \dfrac { 3 } { x } } = \color{#FF6800}{ \dfrac { 11 } { x } } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
 If $\frac{a(x)}{b(x)} = c(x)$ is valid, it is $\begin{cases} a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ x } \left ( \color{#FF6800}{ \dfrac { 11 } { x } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ x } \left ( \color{#FF6800}{ \dfrac { 11 } { x } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Simplify the expression 
$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \\ x \neq 0 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \\ x \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Substitute $x = 4$ for unresolved equations or inequalities 
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = 4 \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
 There are infinitely many solutions if both sides of $\ne$ are different. 
$\begin{cases} x = 4 \\ \text{There are countless solutions} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \\ \text{There are countless solutions} \end{cases}$
 Ignore the cases where the system of equations where there are infinitely many solutions. 
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 }$
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