4.
![y=\sqrt[4]{x^2-5x+6}+ \frac{\sqrt[5]{x+3}}{\sqrt{-x+2}}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B4%5D%7Bx%5E2-5x%2B6%7D%2B%20%5Cfrac%7B%5Csqrt%5B5%5D%7Bx%2B3%7D%7D%7B%5Csqrt%7B-x%2B2%7D%7D "y=\sqrt[4]{x^2-5x+6}+ \frac{\sqrt[5]{x+3}}{\sqrt{-x+2}}")
Обл. Опр.
x\\xe(-\infty;2]V[3;+\infty)" alt="x^2-5x+6\geq 0\\(x-3)(x-2)\geq 0\\+++[2]---[3]+++>x\\xe(-\infty;2]V[3;+\infty)" align="absmiddle" class="latex-formula">
0\\x<2" alt="-x+2>0\\x<2" align="absmiddle" class="latex-formula">
Объединим условия, получим:
5.
![\frac{\sqrt[3]{a^2}-2\sqrt[3]{ab}}{\sqrt[3]{a^2}-4\sqrt[3]{ab}+4\sqrt[3]{b^2}} =\frac{\sqrt[3]{a}(\sqrt[3]{a}-2\sqrt[3]{b})}{(\sqrt[3]{a}-2\sqrt[3]{b})^2} =\frac{\sqrt[3]{a}}{\sqrt[3]{a}-\sqrt[3]{b}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7Ba%5E2%7D-2%5Csqrt%5B3%5D%7Bab%7D%7D%7B%5Csqrt%5B3%5D%7Ba%5E2%7D-4%5Csqrt%5B3%5D%7Bab%7D%2B4%5Csqrt%5B3%5D%7Bb%5E2%7D%7D%20%3D%5Cfrac%7B%5Csqrt%5B3%5D%7Ba%7D%28%5Csqrt%5B3%5D%7Ba%7D-2%5Csqrt%5B3%5D%7Bb%7D%29%7D%7B%28%5Csqrt%5B3%5D%7Ba%7D-2%5Csqrt%5B3%5D%7Bb%7D%29%5E2%7D%20%3D%5Cfrac%7B%5Csqrt%5B3%5D%7Ba%7D%7D%7B%5Csqrt%5B3%5D%7Ba%7D-%5Csqrt%5B3%5D%7Bb%7D%7D "\frac{\sqrt[3]{a^2}-2\sqrt[3]{ab}}{\sqrt[3]{a^2}-4\sqrt[3]{ab}+4\sqrt[3]{b^2}} =\frac{\sqrt[3]{a}(\sqrt[3]{a}-2\sqrt[3]{b})}{(\sqrt[3]{a}-2\sqrt[3]{b})^2} =\frac{\sqrt[3]{a}}{\sqrt[3]{a}-\sqrt[3]{b}}")