Answer:
5 + 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Given
[tex]\frac{\sqrt{3}+\sqrt{2} }{\sqrt{3}-\sqrt{2} }[/tex]
Multiply numerator/ denominator by the conjugate of the denominator
The conjugate of [tex]\sqrt{3}[/tex] - [tex]\sqrt{2}[/tex] is [tex]\sqrt{3}[/tex] + [tex]\sqrt{2}[/tex]
= [tex]\frac{(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2}) }{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{3+\sqrt{6} +\sqrt{6}+2 }{3-2}[/tex]
= [tex]\frac{5+2\sqrt{6} }{1}[/tex]
= 5 + 2[tex]\sqrt{6}[/tex] → with a = 5 and b = 2
