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вынесем за скобки множитель х и затем умножим числитель и знаменатель на сопряженное
![\displaystyle z\cdot \bigg( \frac{(4+z)(2- \sqrt{4+z} )}{2^2-( \sqrt{4+z})^2} + \frac{(4-z)(2+ \sqrt{4+z})}{2^2-( \sqrt{4+z})^2} +4\bigg)=\\ \\ \\ =z\cdot\bigg( \frac{(4+z)(2- \sqrt{4+z})}{4-4-z} + \frac{(4-z)(2+ \sqrt{4+z})}{4-4-z} +4\bigg)=\\ \\ \\ =z\cdot\bigg( \frac{-8+4\sqrt{4+z}-2z+z\sqrt{4+z}-8-4\sqrt{4+z}+2z+z\sqrt{4+z}}{z}+4\bigg)=\\ \\ \\ =-16+2z\sqrt{4+z}+4z \displaystyle z\cdot \bigg( \frac{(4+z)(2- \sqrt{4+z} )}{2^2-( \sqrt{4+z})^2} + \frac{(4-z)(2+ \sqrt{4+z})}{2^2-( \sqrt{4+z})^2} +4\bigg)=\\ \\ \\ =z\cdot\bigg( \frac{(4+z)(2- \sqrt{4+z})}{4-4-z} + \frac{(4-z)(2+ \sqrt{4+z})}{4-4-z} +4\bigg)=\\ \\ \\ =z\cdot\bigg( \frac{-8+4\sqrt{4+z}-2z+z\sqrt{4+z}-8-4\sqrt{4+z}+2z+z\sqrt{4+z}}{z}+4\bigg)=\\ \\ \\ =-16+2z\sqrt{4+z}+4z](https://tex.z-dn.net/?f=%5Cdisplaystyle+z%5Ccdot+%5Cbigg%28+%5Cfrac%7B%284%2Bz%29%282-+%5Csqrt%7B4%2Bz%7D+%29%7D%7B2%5E2-%28+%5Csqrt%7B4%2Bz%7D%29%5E2%7D+%2B+%5Cfrac%7B%284-z%29%282%2B+%5Csqrt%7B4%2Bz%7D%29%7D%7B2%5E2-%28+%5Csqrt%7B4%2Bz%7D%29%5E2%7D+%2B4%5Cbigg%29%3D%5C%5C+%5C%5C+%5C%5C+%3Dz%5Ccdot%5Cbigg%28+%5Cfrac%7B%284%2Bz%29%282-+%5Csqrt%7B4%2Bz%7D%29%7D%7B4-4-z%7D+%2B+%5Cfrac%7B%284-z%29%282%2B+%5Csqrt%7B4%2Bz%7D%29%7D%7B4-4-z%7D+%2B4%5Cbigg%29%3D%5C%5C+%5C%5C+%5C%5C+%3Dz%5Ccdot%5Cbigg%28+%5Cfrac%7B-8%2B4%5Csqrt%7B4%2Bz%7D-2z%2Bz%5Csqrt%7B4%2Bz%7D-8-4%5Csqrt%7B4%2Bz%7D%2B2z%2Bz%5Csqrt%7B4%2Bz%7D%7D%7Bz%7D%2B4%5Cbigg%29%3D%5C%5C+%5C%5C+%5C%5C+%3D-16%2B2z%5Csqrt%7B4%2Bz%7D%2B4z)
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