Answer:
Step-by-step explanation:
[tex]\[\frac{1+2\sqrt{-3} }{1+\sqrt{-3} } =\frac{1+2\sqrt{-3} }{1+\sqrt{-3} } \times \frac{1-\sqrt{-3} }{1-\sqrt{-3} } =\frac{(1+2\sqrt{-3})(1-\sqrt{-3} ) }{1^{2}-(\sqrt{-3})^{2} } =\frac{1+2\sqrt{-3}-\sqrt{-3}-2(\sqrt{-3} )^{2} }{4} =\frac{1+\sqrt{-3}+6 }{4} =\frac{7+\sqrt{-3} }{4} \][/tex]
