#### Answer

$\displaystyle y' = \frac{e^{x}(x+3) - x^{2}(1+2e^{x})}{(2e^{x}-x)^{2}}$

#### Work Step by Step

$y = \frac{x^{2}+3e^{x}}{2e^{x}-x}$
$y' = \frac{(2e^{x}-x)(2x +3e^{x}) - (x^{2}+3e^{x})(2e^{x}-1)}{(2e^{x}-x)^{2}}$
$y' = \frac{xe^{x}-x^{2}-2x^{2}e^{x}+3e^{x}}{(2e^{x}-x)^{2}}$
$y' = \frac{e^{x}(x+3) - x^{2}(1+2e^{x})}{(2e^{x}-x)^{2}}$