`
$
\eqalign{\frac{{2x + 1}}
{{x^2 - 2}} = 0}
$
$
\eqalign{\frac{A}
{B} = 0 \to A = 0}
$
$
2x + 1 = 0
$
$
\eqalign{\frac{{2x - 1}}
{{x^2 - 2}} = x}
$
$
\eqalign{\frac{A}
{B} = C \to A = BC}
$
$
2x - 1 = x\left( {x^2 - 2} \right)
$
$
\eqalign{\frac{{2x - 1}}
{{x^2 - 2}} = \frac{{2x - 1}}
{{x^3 }}}
$
$
\eqalign{\frac{A}
{B} = \frac{A}
{C} \to A = 0 \vee B = C}
$
$
2x - 1 = 0 \vee x^2 - 2 = x^3
$
$
\eqalign{\frac{{2x - 1}}
{{x^2 - 2}} = \frac{3}
{{x^3 }}}
$
$
\eqalign{\frac{A}
{B} = \frac{C}
{D} \to AD = BC}
$
$
x^3 \left( {2x - 1} \right) = 3\left( {x^2 - 2} \right)
$
$
\eqalign{\frac{{2x - 1}}
{{x^2 - 2}} = \frac{3}
{{x^2 - 2}}}
$
$
\eqalign{\frac{A}
{B} = \frac{C}
{B} \to A = C}
$
$
2x - 1 = 3
$