Subtract (2)/(4+sqrt6) - (2)/(4-sqrt6).
Can someone explain how to do this to me?
3 answers
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.
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
thank you
1 answer