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Rasionalisasi...
![\displaystyle\sf \frac{\sqrt{5^{2019}}}{\sqrt{5^{2019}}-\sqrt{5^{2015}}}=\\\\\\\frac{\sqrt{5^{2019}}}{\sqrt{5^{2019}}-\sqrt{5^{2015}}}\times \frac{\sqrt{5^{2019}}+\sqrt{5^{2015}}}{\sqrt{5^{2019}}+\sqrt{5^{2015}}}=\\\\\\\frac{(\sqrt{5^{2019}})^2+\sqrt{5^{2019}}(\sqrt{5^{2015}})}{(\sqrt{5^{2019}})^2-(\sqrt{5^{2015}})^2}=\\\\\\\frac{5^{2019}+\sqrt{5^{2019}\cdot5^{2015}}}{5^{2019}-5^{2015}}=\\\\\\\frac{5^{2019}+\sqrt{5^{2019+2015}}}{5^{2019}-5^{2015}}= \displaystyle\sf \frac{\sqrt{5^{2019}}}{\sqrt{5^{2019}}-\sqrt{5^{2015}}}=\\\\\\\frac{\sqrt{5^{2019}}}{\sqrt{5^{2019}}-\sqrt{5^{2015}}}\times \frac{\sqrt{5^{2019}}+\sqrt{5^{2015}}}{\sqrt{5^{2019}}+\sqrt{5^{2015}}}=\\\\\\\frac{(\sqrt{5^{2019}})^2+\sqrt{5^{2019}}(\sqrt{5^{2015}})}{(\sqrt{5^{2019}})^2-(\sqrt{5^{2015}})^2}=\\\\\\\frac{5^{2019}+\sqrt{5^{2019}\cdot5^{2015}}}{5^{2019}-5^{2015}}=\\\\\\\frac{5^{2019}+\sqrt{5^{2019+2015}}}{5^{2019}-5^{2015}}=](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csf%20%5Cfrac%7B%5Csqrt%7B5%5E%7B2019%7D%7D%7D%7B%5Csqrt%7B5%5E%7B2019%7D%7D-%5Csqrt%7B5%5E%7B2015%7D%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B5%5E%7B2019%7D%7D%7D%7B%5Csqrt%7B5%5E%7B2019%7D%7D-%5Csqrt%7B5%5E%7B2015%7D%7D%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B5%5E%7B2019%7D%7D%2B%5Csqrt%7B5%5E%7B2015%7D%7D%7D%7B%5Csqrt%7B5%5E%7B2019%7D%7D%2B%5Csqrt%7B5%5E%7B2015%7D%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%28%5Csqrt%7B5%5E%7B2019%7D%7D%29%5E2%2B%5Csqrt%7B5%5E%7B2019%7D%7D%28%5Csqrt%7B5%5E%7B2015%7D%7D%29%7D%7B%28%5Csqrt%7B5%5E%7B2019%7D%7D%29%5E2-%28%5Csqrt%7B5%5E%7B2015%7D%7D%29%5E2%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B5%5E%7B2019%7D%2B%5Csqrt%7B5%5E%7B2019%7D%5Ccdot5%5E%7B2015%7D%7D%7D%7B5%5E%7B2019%7D-5%5E%7B2015%7D%7D%3D%5C%5C%5C%5C%5C%5C%5Cfrac%7B5%5E%7B2019%7D%2B%5Csqrt%7B5%5E%7B2019%2B2015%7D%7D%7D%7B5%5E%7B2019%7D-5%5E%7B2015%7D%7D%3D)