Answer:
- (4+2sqrt10)/3
Explanation:
The only reason this problem needs to be worked on is that you can't have a radical on the bottom of a fraction(rational expression) . We'll use the CONJUGATE of the denominator(expression on the bottom) to get rid of the radicals.
The conjugate has the same terms as the bottom expression, but it has the OPPOSITE sign in between. Your question has
(root2 - root5). Then the CONJUGATE is
(root2 + root5).
We can't just randomly change the denominator of a number, so we will have to multiply the top by
(root2 + root5) also.
see image.
Multiplying these terms is very similar to multiplying binomials. Use distributive property or, if you know the method, FOIL. You may have learned a box method. This multplication is shown with the arrows in the attached image.
see image.