[tex]( \frac{2x}{2x + y} - \frac{{4x}^{2} }{ {4x}^{2} + 4xy + {y}^{2} } \div ( \frac{2x}{ {4x}^{2} - {y}^{2} } - \frac{1}{2x - y} \\ \frac{2x(2x + y) { - 4x}^{2} }{ {(2x + y)}^{2} } \div \frac{2x - (2x + y)}{(2x - y)(2x + y)} \\ \frac{ {4x}^{2} + 2xy - {4x}^{2} }{ {(2x + y)}^{2} } \div \frac{2x - (2x - y)}{(2x - y)(2x + y)} \\ \frac{2xy}{ {(2x + y)}^{2} } \div \frac{ - y}{(2x - y)(2x + y)} \\ - \frac{2xy}{ {(2x + y)}^{2} } \times \frac{(2x - y)(2x + y)}{y} \\ - \frac{2x}{2x + y} \times (2x - y) \\ \frac{ { - 4x }^{2} - 2xy}{2x + y} \\ \frac{2xy { - 4x}^{2} }{2x + y} [/tex]
