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Formula
Solve the equation
Answer
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Graph
$y = \dfrac { 3 } { 2 }$
$y = \dfrac { - 7 x + 9 } { 3 x }$
Asymptote
$y = - \dfrac { 7 } { 3 }$, $x = 0$
Standard form
$y = \dfrac { 3 } { x } - \dfrac { 7 } { 3 }$
Domain
$y \neq - \dfrac { 7 } { 3 }$
Range
$x \neq 0$
$x$Intercept
$\left ( \dfrac { 9 } { 7 } , 0 \right )$
$\dfrac{ 3 }{ 2 } = \dfrac{ -7x+9 }{ 3x }$
$x = \dfrac { 18 } { 23 }$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { 3 } { 2 } } = \color{#FF6800}{ \dfrac { - 7 x + 9 } { 3 x } }$
$ $ If $ \frac{a(x)}{b(x)} = \frac{c(x)}{d(x)} $ is valid, it is $ \begin{cases} a(x) d(x) = b(x) c(x) \\ b(x) \ne 0 \\ d(x) \ne 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \right ) \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \right ) \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 14 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 14 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \\ 2 \neq 0 \\ 3 x \neq 0 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ 2 \neq 0 \\ 3 x \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Substitute $ x = \dfrac { 18 } { 23 } $ for unresolved equations or inequalities $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 18 } { 23 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 18 } { 23 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ \dfrac { 54 } { 23 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = \dfrac { 18 } { 23 } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \dfrac { 54 } { 23 } \neq 0 \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = \dfrac { 18 } { 23 } \\ \text{There are countless solutions} \\ \dfrac { 54 } { 23 } \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \text{There are countless solutions} \\ \color{#FF6800}{ \dfrac { 54 } { 23 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \color{#FF6800}{ \dfrac { 54 } { 23 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = \dfrac { 18 } { 23 } \\ \color{#FF6800}{ \dfrac { 54 } { 23 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = \dfrac { 18 } { 23 } \\ \text{There are countless solutions} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } } \\ \text{There are countless solutions} \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 18 } { 23 } }$
$ $ 그래프 보기 $ $
Graph
Solution search results
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