Verified answer

Объяснение:

[tex]\frac{4}{\sqrt{3}-1 } =\frac{4*(\sqrt{3}+1) }{(\sqrt{3} -1)*(\sqrt{3}+1) }= \frac{4*(\sqrt{3}+1) }{(\sqrt{3})^2 -1^2} =\frac{4*(\sqrt{3}+1) }{3-1}=\frac{4*(\sqrt{3}+1) }{2}=2*(\sqrt{3}+1).[/tex]

[tex]\displaystyle\bf\\\frac{4}{\sqrt{3} -1} =\frac{4\cdot(\sqrt{3} +1)}{(\sqrt{3} -1)(\sqrt{3}+1) }=\frac{4\cdot(\sqrt{3}+1) }{(\sqrt{3})^{2} -1^{2} } =\frac{4\cdot(\sqrt{3} +1)}{3-1} = \\\\\\=\frac{4\cdot(\sqrt{3} +1)}{2} = 2(\sqrt{3} +1)[/tex]