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Formula
Judge the identity
Answer
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Solve the equation
Answer
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$x = \dfrac{ x }{ a } +b$
$\begin{cases} \dfrac { 1 } { a } = 1 \\ b = 0 \end{cases}$
Compare coefficients to find unknowns
$x = \color{#FF6800}{ \dfrac { x } { a } } \color{#FF6800}{ + } \color{#FF6800}{ b }$
$ $ Organize the expression $ $
$x = \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { x } { a } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { x } { a } }$
$ $ Compare the coefficients to form a system of equations $ $
$\begin{cases} \color{#FF6800}{ \dfrac { 1 } { a } } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ b } = \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x + a b = a x \\ a \neq 0 \end{cases}$
Solve the fractional equation
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { x } { a } } \color{#FF6800}{ + } \color{#FF6800}{ b }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { x + a b } { a } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { x + a b } { a } }$
$ $ Reverse the left and right terms of the equation (or inequality) $ $
$\color{#FF6800}{ \dfrac { x + a b } { a } } = \color{#FF6800}{ x }$
$\color{#FF6800}{ \dfrac { x + a b } { a } } = \color{#FF6800}{ x }$
$ $ 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}$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ b } = \color{#FF6800}{ a } \color{#FF6800}{ x } \\ \color{#FF6800}{ a } \neq \color{#FF6800}{ 0 } \end{cases}$
Solution search results
search-thumbnail-$i\right)$ $\dfrac {x} {a}+b=\dfrac {x} {b}+a$
7th-9th grade
Algebra
search-thumbnail-$8$ $y$ $\dfrac {x} {a}+\dfrac {y} {b}=\dfrac {1} {a}+\dfrac {1} {b}$ 
$\dfrac {x} {a}-\dfrac {y} {b}=\dfrac {1} {a}-\dfrac {1} {b}$
7th-9th grade
Algebra
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