Question

divide and rationalize 5+sqrt(7)/18-sqrt(3) show all work please

Answer 1

\[\frac{5+\sqrt7}{18-\sqrt3}\]
\[=\frac{5+\sqrt7}{18-\sqrt3}\times \frac{18+\sqrt3}{18+\sqrt3}\] is a start, i.e. multiply top and bottom by the conjugate of the denominator

Answer 2

this works because \((a+b)(a-b)=a^2-b^2\) making your denominator
\[18^2-(\sqrt{3})^2=324-3=321\] and now there is no radical in the denominator

Answer 3

you get
\[\frac{(5+\sqrt7)(18+\sqrt3)}{321}\] and your last job is to multiply out in the numerator

Answer 4

How do you multiply out the numerator?