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\displaystyle \dfrac{3}{x+8}

=

\displaystyle \dfrac{1}{2x+1}

\displaystyle \cdot(x+8)

\displaystyle 3

=

\displaystyle \dfrac{1\cdot(x+8)}{2x+1}

\displaystyle \cdot (2x+1)

\displaystyle 3\cdot (2x+1)

=

\displaystyle x+8

\displaystyle 6x+3

=

\displaystyle x+8

\displaystyle -x

\displaystyle 5x+3

=

\displaystyle 8

\displaystyle -3

\displaystyle 5x

=

\displaystyle 5

\displaystyle :5

\displaystyle x

=

\displaystyle 1

$\displaystyle \dfrac{3}{x+8}$	$=$	$\displaystyle \dfrac{1}{2x+1}$	$\displaystyle \cdot(x+8)$
	↓	multipliziere und kürze
$\displaystyle 3$	$=$	$\displaystyle \dfrac{1\cdot(x+8)}{2x+1}$	$\displaystyle \cdot (2x+1)$
	↓	multipliziere und kürze
$\displaystyle 3\cdot (2x+1)$	$=$	$\displaystyle x+8$
$\displaystyle 6x+3$	$=$	$\displaystyle x+8$	$\displaystyle -x$
	↓	subtrahiere
$\displaystyle 5x+3$	$=$	$\displaystyle 8$	$\displaystyle -3$
	↓	subtrahiere
$\displaystyle 5x$	$=$	$\displaystyle 5$	$\displaystyle :5$
	↓	kürze
$\displaystyle x$	$=$	$\displaystyle 1$