Zad. na nudę
14.
Uprość wyrażenie:![( \frac{ \sqrt[4]{x^3}- \sqrt[4]{x} }{1- \sqrt{x} } + \frac{1+ \sqrt{x} }{ \sqrt[4]{x} } )^{^2}*(1+ \frac{2}{ \sqrt{x} } + \frac{1}{x} )^{^{- \frac{1}{2}](https://tex.z-dn.net/?f=%28+%5Cfrac%7B+%5Csqrt%5B4%5D%7Bx%5E3%7D-+%5Csqrt%5B4%5D%7Bx%7D+%7D%7B1-+%5Csqrt%7Bx%7D+%7D+%2B+%5Cfrac%7B1%2B+%5Csqrt%7Bx%7D+%7D%7B+%5Csqrt%5B4%5D%7Bx%7D+%7D+%29%5E%7B%5E2%7D%2A%281%2B+%5Cfrac%7B2%7D%7B+%5Csqrt%7Bx%7D+%7D+%2B+%5Cfrac%7B1%7D%7Bx%7D+%29%5E%7B%5E%7B-+%5Cfrac%7B1%7D%7B2%7D+ "( \frac{ \sqrt[4]{x^3}- \sqrt[4]{x} }{1- \sqrt{x} } + \frac{1+ \sqrt{x} }{ \sqrt[4]{x} } )^{^2}*(1+ \frac{2}{ \sqrt{x} } + \frac{1}{x} )^{^{- \frac{1}{2}")
14.
Uprość wyrażenie:
jestemt
![(\frac{\sqrt[4]{x^3}-\sqrt[4]x}{1-\sqrt{x}}+\frac{1+\sqrt{x}}{\sqrt[4]{x}})^2*(1+\frac2{\sqrt{x}}+\frac1{x})^{-\frac12} = (\frac{\sqrt[4]{x}(\sqrt[4]{x^3}-\sqrt[4]{x})+(1-\sqrt{x})(1+\sqrt{x})}{\sqrt[4]{x}*(1-\sqrt{x})})^2\\\\ *(\frac{x+2\sqrt{x}+1}{x})^{-\frac12} = (\frac{x-\sqrt{x}+1-x}{\sqrt[4]{x}(1-\sqrt{x})})^2*(\frac{x}{x+2\sqrt{x}+1})^{\frac12} = \frac{(1-\sqrt{x})^2}{\sqrt{x}(1-\sqrt{x})^2}*\frac{\sqrt{x}}{\sqrt{(\sqrt{x}+1)^2}}\\\\= \frac{1}{\sqrt{x}+1} = \frac{\sqrt{x}-1}{x-1}](https://tex.z-dn.net/?f=%28%5Cfrac%7B%5Csqrt%5B4%5D%7Bx%5E3%7D-%5Csqrt%5B4%5Dx%7D%7B1-%5Csqrt%7Bx%7D%7D%2B%5Cfrac%7B1%2B%5Csqrt%7Bx%7D%7D%7B%5Csqrt%5B4%5D%7Bx%7D%7D%29%5E2%2A%281%2B%5Cfrac2%7B%5Csqrt%7Bx%7D%7D%2B%5Cfrac1%7Bx%7D%29%5E%7B-%5Cfrac12%7D+%3D+%28%5Cfrac%7B%5Csqrt%5B4%5D%7Bx%7D%28%5Csqrt%5B4%5D%7Bx%5E3%7D-%5Csqrt%5B4%5D%7Bx%7D%29%2B%281-%5Csqrt%7Bx%7D%29%281%2B%5Csqrt%7Bx%7D%29%7D%7B%5Csqrt%5B4%5D%7Bx%7D%2A%281-%5Csqrt%7Bx%7D%29%7D%29%5E2%5C%5C%5C%5C+%2A%28%5Cfrac%7Bx%2B2%5Csqrt%7Bx%7D%2B1%7D%7Bx%7D%29%5E%7B-%5Cfrac12%7D+%3D+%28%5Cfrac%7Bx-%5Csqrt%7Bx%7D%2B1-x%7D%7B%5Csqrt%5B4%5D%7Bx%7D%281-%5Csqrt%7Bx%7D%29%7D%29%5E2%2A%28%5Cfrac%7Bx%7D%7Bx%2B2%5Csqrt%7Bx%7D%2B1%7D%29%5E%7B%5Cfrac12%7D+%3D+%5Cfrac%7B%281-%5Csqrt%7Bx%7D%29%5E2%7D%7B%5Csqrt%7Bx%7D%281-%5Csqrt%7Bx%7D%29%5E2%7D%2A%5Cfrac%7B%5Csqrt%7Bx%7D%7D%7B%5Csqrt%7B%28%5Csqrt%7Bx%7D%2B1%29%5E2%7D%7D%5C%5C%5C%5C%3D+%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%2B1%7D+%3D+%5Cfrac%7B%5Csqrt%7Bx%7D-1%7D%7Bx-1%7D "(\frac{\sqrt[4]{x^3}-\sqrt[4]x}{1-\sqrt{x}}+\frac{1+\sqrt{x}}{\sqrt[4]{x}})^2*(1+\frac2{\sqrt{x}}+\frac1{x})^{-\frac12} = (\frac{\sqrt[4]{x}(\sqrt[4]{x^3}-\sqrt[4]{x})+(1-\sqrt{x})(1+\sqrt{x})}{\sqrt[4]{x}*(1-\sqrt{x})})^2\\\\ *(\frac{x+2\sqrt{x}+1}{x})^{-\frac12} = (\frac{x-\sqrt{x}+1-x}{\sqrt[4]{x}(1-\sqrt{x})})^2*(\frac{x}{x+2\sqrt{x}+1})^{\frac12} = \frac{(1-\sqrt{x})^2}{\sqrt{x}(1-\sqrt{x})^2}*\frac{\sqrt{x}}{\sqrt{(\sqrt{x}+1)^2}}\\\\= \frac{1}{\sqrt{x}+1} = \frac{\sqrt{x}-1}{x-1}")
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