Resolva, em $\mathbb{R}$, a equação

\[\begin{array}{*{20}{l}}{\frac{{2x + 4}}{{\mathop {x{\rm{ }} – {\rm{ }}3}\limits_{\left( {x + 5} \right)} }} = \frac{{x – 2}}{{\mathop {x{\rm{ }} + {\rm{ }}5}\limits_{\left( {x – 3} \right)} }}}& \Leftrightarrow &{\frac{{2{x^2} + 10x + 4x + 20 – {x^2} + 3x + 2x – 6}}{{\left( {x – 3} \right)\left( {5 + 5} \right)}} = 0}\\{}& \Leftrightarrow &{\frac{{{x^2} + 19x + 14}}{{\left( {x – 3} \right)\left( {5 + 5} \right)}} = 0}\\{}& \Leftrightarrow &{\begin{array}{*{20}{l}}{{x^2} + 19x + 14 = 0}& \wedge &{\left( {x – 3} \right)\left( {5 + 5} \right) \ne 0}\end{array}}\\{}& \Leftrightarrow &{\begin{array}{*{20}{l}}{x = \frac{{ – 19 \pm \sqrt {361 – 56} }}{2}}& \wedge &{\begin{array}{*{20}{c}}{x \ne 3}& \wedge &{x \ne  – 5}\end{array}}\end{array}}\\{}& \Leftrightarrow &{\begin{array}{*{20}{l}}{x = \frac{{ – 19 – \sqrt {305} }}{2}}& \vee &{x = \frac{{ – 19 + \sqrt {305} }}{2}}\end{array}}\end{array}\]