SOLUTION: Simplify to the end and write as a single fraction (no radicals in the denominators) Please show work. ((1)/(x-√3))+((1)/(x+√3))

Algebra ->  Radicals -> SOLUTION: Simplify to the end and write as a single fraction (no radicals in the denominators) Please show work. ((1)/(x-√3))+((1)/(x+√3))       Log On


   

Question 1014561: Simplify to the end and write as a single fraction (no radicals in the denominators) Please show work.
((1)/(x-√3))+((1)/(x+√3))
Found 3 solutions by rothauserc, ikleyn, macston:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(1 / (x-sqrt(3)) + (1 / (x+sqrt(3))
the GCF for the denominator is (x^2 - 3)
(((x+sqrt(3)) + ((x-sqrt(3))) / (x^2 - 3) =
2x / (x^2 - 3)

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Simplify to the end and write as a single fraction (no radicals in the denominators) Please show work.
((1)/(x-sqrt(3)) + ((1)/(x+sqrt(3)))
--------------------------------------- 

1%2F%28x-sqrt%283%29%29 + 1%2F%28x%2Bsqrt%283%29%29 =    (write with the common denominator)


= %28x%2Bsqrt%283%29%29%2F%28%28x-sqrt%283%29%29%2A%28x%2Bsqrt%283%29%29%29 + %28x-sqrt%283%29%29%2F%28%28x-sqrt%283%29%29%2A%28x%2Bsqrt%283%29%29%29 = 


= %28x%2Bsqrt%283%29+%2B+x+-sqrt%283%29%29%2F%28%28x-sqrt%283%29%29%2A%28x%2Bsqrt%283%29%29%29 = 


= %282x%29%2F%28x%5E2+-+%28sqrt%283%29%29%5E2%29 = %282x%29%2F%28x%5E2+-+3%29.


Answer by macston(5194) About Me  (Show Source):