Thực hiện phép tính: g) x/( x − 2 y) + x/( x + 2 y) + 4 x y/( 4 y ^2 − x ^2) .

g) \[\frac{x}{{x - 2y}} + \frac{x}{{x + 2y}} + \frac{{4xy}}{{4{y^2} - {x^2}}}\]

\[ = \frac{x}{{x - 2y}} + \frac{x}{{x + 2y}} - \frac{{4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\]

\[ = \frac{{x\left( {x + 2y} \right) + x\left( {x - 2y} \right) - 4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\]

\[ = \frac{{{x^2} + 2xy + {x^2} - 2xy - 4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\]

\[ = \frac{{2{x^2} - 4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\]

\[ = \frac{{2x\left( {x - 2y} \right)}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}} = \frac{{2x}}{{x + 2y}}.\]