Raționalizăm numitorii și aducem la același numitor comun:
[tex]= \bigg(\dfrac{9\sqrt{2} }{4\cdot2} + \dfrac{4\sqrt{2} }{3\cdot2}\bigg) - \bigg(\dfrac{16\sqrt{2} }{3\cdot2} + \dfrac{7\sqrt{2} }{4\cdot2} - \dfrac{5\sqrt{2} }{2}\bigg) =\\[/tex]
numitorul comun este 24
[tex]= \bigg(\dfrac{^{3)} 9\sqrt{2} }{8} + \dfrac{^{8)} 2\sqrt{2} }{3}\bigg) - \bigg(\dfrac{^{8)} 8\sqrt{2} }{3} + \dfrac{^{3)} 7\sqrt{2} }{8} - \dfrac{^{12)} 5\sqrt{2} }{2}\bigg)\\[/tex]
[tex]= \bigg(\dfrac{27\sqrt{2} }{24} + \dfrac{16\sqrt{2} }{24}\bigg) - \bigg(\dfrac{64\sqrt{2} }{24} + \dfrac{21\sqrt{2} }{24} - \dfrac{60\sqrt{2} }{24}\bigg)\\[/tex]
[tex]= \dfrac{43\sqrt{2} }{24} - \dfrac{25\sqrt{2} }{24} = \dfrac{18\sqrt{2} }{24} = \dfrac{3\sqrt{2} }{4}[/tex]
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Raționalizăm numitorii și aducem la același numitor comun:
[tex]= \bigg(\dfrac{9\sqrt{2} }{4\cdot2} + \dfrac{4\sqrt{2} }{3\cdot2}\bigg) - \bigg(\dfrac{16\sqrt{2} }{3\cdot2} + \dfrac{7\sqrt{2} }{4\cdot2} - \dfrac{5\sqrt{2} }{2}\bigg) =\\[/tex]
numitorul comun este 24
[tex]= \bigg(\dfrac{^{3)} 9\sqrt{2} }{8} + \dfrac{^{8)} 2\sqrt{2} }{3}\bigg) - \bigg(\dfrac{^{8)} 8\sqrt{2} }{3} + \dfrac{^{3)} 7\sqrt{2} }{8} - \dfrac{^{12)} 5\sqrt{2} }{2}\bigg)\\[/tex]
[tex]= \bigg(\dfrac{27\sqrt{2} }{24} + \dfrac{16\sqrt{2} }{24}\bigg) - \bigg(\dfrac{64\sqrt{2} }{24} + \dfrac{21\sqrt{2} }{24} - \dfrac{60\sqrt{2} }{24}\bigg)\\[/tex]
[tex]= \dfrac{43\sqrt{2} }{24} - \dfrac{25\sqrt{2} }{24} = \dfrac{18\sqrt{2} }{24} = \dfrac{3\sqrt{2} }{4}[/tex]