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-$$\frac{(1 + x)\sqrt[3]{1 + x} - 1}{(\sqrt[3]{1 + x} + 1) \cdot (\sqrt[3]{(1 + x)^2} + 1)} $$ + \frac{\sqrt[3]{(1 + x)^2} + \sqrt[3]{1 + x} + 1}{ \sqrt[3]{(1 + x)^2} + \sqrt[3]{1 + x} + 1} = \frac{(1 + x) - 1}{\sqrt[3]{(1 + x)^2} + \sqrt[3]{1 + x} + 1} =$$ +$$ \frac{x}{\sqrt[3]{(1 + x)^2} + \sqrt[3]{1 + x} + 1} $$ \subsection*{Point b)} $$ \frac{1 - cos(x)}{sin(x)} = \frac{sin^2(x)cos^2(x) - cos(x)}{sin(x)} \cdot \frac{sin(x)}{cos(x)} \cdot \frac{cos(x)}{sin(x)} = (sin^2(x)cos(x) - 1)\cdot\frac{cos(x)}{sin(x)}$$ \subsection*{Point c)} -$$ \frac{1}{1-\sqrt{x^2-1}} = \frac{x}{x^2-\sqrt{x^4-x^2}}$$ +$$ \frac{1}{1-\sqrt{x^2-1}} = \frac{1+\sqrt{x^2-1}}{(1-\sqrt{x^2-1})(1+\sqrt{x^2-1})} = +\frac{1+\sqrt{x^2-1}}{1 - (x^2-1)} = -\frac{1+\sqrt{x^2-1}}{x^2} $$ \subsection*{Point d)} $$ x^3\cdot\left(\frac{x}{x^2-1}-\frac{1}{x}\right) = x^3\cdot\left(\frac{x^2-x^2+1}{x^3-x}\right) = \frac{x^2}{x^2-1}$$