Đáp án:
$\begin{array}{l}
1)a)5x - 3 = 12\\
\Rightarrow 5x = 15\\
\Rightarrow x = 3\\
b)\frac{3}{{x + 1}} = \frac{2}{{x + 2}}\left( {dk:x \ne - 1;x \ne - 2} \right)\\
\Rightarrow 3\left( {x + 2} \right) = 2\left( {x + 1} \right)\\
\Rightarrow x = - 4\left( {tmdk} \right)\\
2)\\
a)Xét\,\Delta ABE;\Delta ACF:\\
+ \widehat {BAE}\,chung\\
+ \widehat {AEB} = \widehat {AFC} = {90^0}\\
\Rightarrow \Delta ABE \sim \Delta ACF\left( {g - g} \right)\\
b)Do:\Delta ABE \sim \Delta ACF\\
\Rightarrow \frac{{AB}}{{AC}} = \frac{{AE}}{{AF}}\\
\Rightarrow AE.AC = AF.AB
\end{array}$