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Formula
Solve the equation
Answer
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Graph
$y = \dfrac { 48 } { x }$
$y = - 4$
Asymptote
$y = 0$, $x = 0$
Standard form
$y = \dfrac { 48 } { x }$
Domain
$y \neq 0$
Range
$x \neq 0$
$\dfrac{ 48 }{ x } = -4$
$x = - 12$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { 48 } { x } } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$ $ 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}$
$\begin{cases} \color{#FF6800}{ 48 } = \color{#FF6800}{ x } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 48 } = \color{#FF6800}{ x } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ 48 } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 48 } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \\ x \neq 0 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \\ x \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Substitute $ x = - 12 $ for unresolved equations or inequalities $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 12 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = - 12 \\ \color{#FF6800}{ - } \color{#FF6800}{ 12 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ If $ -f(x) \ne 0 $ is valid, it is $ f(x) \ne 0$
$\begin{cases} x = - 12 \\ \color{#FF6800}{ 12 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = - 12 \\ \color{#FF6800}{ 12 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = - 12 \\ \text{해가 무수히 많습니다} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \\ \text{해가 무수히 많습니다} \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
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