Question
Solve equation by factorization : $3 x-\frac{8}{x}=2$
✓
Answer
$
\begin{aligned}
& 3 x-\frac{8}{x}=2 \\
& \frac{3 x^2-8}{x}=2 \\
& \Rightarrow 3 x^2-8=2 x \\
& \Rightarrow 3 x^2-2 x-8=0 \\
& \Rightarrow 3 x^2-6 x+4 x-8=0 \\
& \Rightarrow 3 x(x-2)+4(x-2)=0 \\
& \Rightarrow(x-2)(3 x+4)=0
\end{aligned}
$
Either $x-2=0$,
then $x=2$
or
$
3 x+4=0 \text {, }
$
then $3 x=-4$
$
\Rightarrow x =\frac{-4}{3}
$
Hence $x=2, \frac{-4}{3}$.
\begin{aligned}
& 3 x-\frac{8}{x}=2 \\
& \frac{3 x^2-8}{x}=2 \\
& \Rightarrow 3 x^2-8=2 x \\
& \Rightarrow 3 x^2-2 x-8=0 \\
& \Rightarrow 3 x^2-6 x+4 x-8=0 \\
& \Rightarrow 3 x(x-2)+4(x-2)=0 \\
& \Rightarrow(x-2)(3 x+4)=0
\end{aligned}
$
Either $x-2=0$,
then $x=2$
or
$
3 x+4=0 \text {, }
$
then $3 x=-4$
$
\Rightarrow x =\frac{-4}{3}
$
Hence $x=2, \frac{-4}{3}$.
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