Question

Subtract (2)/(4+sqrt6) - (2)/(4-sqrt6).

Can someone explain how to do this to me?

Answer 1

Ok, so I tried to work it out myself. I think I have to rationalize the denominator for each fraction and then subtract those two answers.

Answer 2

That would work, but have you noticed that the denominators are conjugates of each other?
so let's do it by finding a common denominator which would be (4+√6)(4-√6) = 16 - 6 = 10
so we have

2/(4+√6) - 2/(4-√6)
= (2(4-√6) - 2(4 +√6) )/10
= (8 - 2√6 - 8 - 2√6)/10
= -4√6/10
= -2√6 /5

Answer 3

thank you