Question

RATIONALIZE THE
Denominator and
simplify

Answer 1

Answer:

$\frac{8-\sqrt{6} }{2}$

Step-by-step explanation:

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator, which in this is 2 - √6.

We can write the expression:

$\frac{3\sqrt{6}+5 }{2+\sqrt{6}} *\frac{2-\sqrt{6}}{2-\sqrt{6} }$

We can use the special product of the difference of squares to simplify the denominator:

$(2 + \sqrt{6})(2-\sqrt{6}) = 2^2 - (\sqrt{6})^2 =4 - 6 = -2$

We can use distributive for the numerator:

$(3\sqrt{6}+5)(2-\sqrt{6})=6\sqrt{6} -18+ 10-5\sqrt{6} =\sqrt{6} -8$

Now we can rewrite the fraction:

$\frac{\sqrt{6}-8 }{-2} =\frac{8-\sqrt{6} }{2}$