[tex]a > 0 \: \: , \: b > 0 \\ \frac{4a - b}{ 2\sqrt{a} + \sqrt{b} } = \frac{(2 \sqrt{a}) {}^{2} - ( \sqrt{b} ) {}^{2}}{2 \sqrt{a} + \sqrt{b} } = \\ = \frac{(2 \sqrt{a} - \sqrt{b})(2 \sqrt{a} + \sqrt{b}) }{2 \sqrt{a} + \sqrt{b} } = 2 \sqrt{a} - \sqrt{b} [/tex]

[tex]\displaystyle\bf\\\frac{4a-b}{2\sqrt{a} +\sqrt{b} } =\frac{(2\sqrt{a} )^{2} -(\sqrt{b} )^{2} }{2\sqrt{a} +\sqrt{b} } =\\\\\\=\frac{(2\sqrt{a} -\sqrt{b} )\cdot(2\sqrt{a} +\sqrt{b} )}{2\sqrt{a} +\sqrt{b} } =2\sqrt{a} -\sqrt{b}[/tex]