Answer: [tex]\sqrt{5} + \sqrt{3} + 10 + 2\sqrt{15}[/tex]
Step-by-step explanation:
[tex]\frac{2+4\sqrt{5} }{\sqrt{5}-\sqrt{3} }[/tex]
You need to multiply by the conjugate
To find the conjugate, first remember:
(a+b)(a-b) = a^2 - b^2 (if a and b are sqrts, this will eliminate the square roots, rationalizing the denominator)
You have √5 - √3 as the denominator
You should multiply by √5 + √3
(This will eliminate the sqrts)
Remember to multiply both the numerator and denominator
[tex]\frac{2+4\sqrt{5} }{\sqrt{5}-\sqrt{3} } = \frac{2+4\sqrt{5} }{\sqrt{5}-\sqrt{3} } * \frac{\sqrt{5}+\sqrt{3} }{\sqrt{5}+\sqrt{3}}[/tex]
Now simplify
[tex]\frac{2+4\sqrt{5} }{\sqrt{5}-\sqrt{3} } * \frac{\sqrt{5}+\sqrt{3} }{\sqrt{5}+\sqrt{3}} = \frac{(2+4\sqrt{5})(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})} = \frac{2\sqrt{5}+2\sqrt{3}+20+4\sqrt{15}}{5-3} = \sqrt{5} + \sqrt{3} + 10 + 2\sqrt{15}[/tex]
