Question
Subtract (2)/(4+sqrt6) - (2)/(4-sqrt6).
Can someone explain how to do this to me?
Can someone explain how to do this to me?
Answers
Nickie
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.
Reiny
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
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
Karizzma
thank you