SOLUTION: I need help with this rational equation, [1/(x-2)]-(5/1)=1/(x+2) The answer is supposed to be: +,- [2sqrt(30)]/5 I always get an quadratic equation like 5x^2-20=0 (cant us

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this rational equation, [1/(x-2)]-(5/1)=1/(x+2) The answer is supposed to be: +,- [2sqrt(30)]/5 I always get an quadratic equation like 5x^2-20=0 (cant us      Log On


   

Question 435795: I need help with this rational equation,
[1/(x-2)]-(5/1)=1/(x+2)
The answer is supposed to be: +,- [2sqrt(30)]/5
I always get an quadratic equation like 5x^2-20=0 (cant use the formula).
Thank you!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

1%2F%28x-2%29-%285%2F1%29=1%2F%28x%2B2%29

  (x+2) - 5(x+2)(x-2) = (x-2)

  x+2 -5x^2 + 20 = x-2

       24 = 5x^2  | note the 24

       x^2 = 24/5  

       x = ± sqrt%2824%29%2Fsqrt%285%29

       x = ± sqrt%284%2A6%29%2Fsqrt%285%29

       x = ± %282%2F5%29%2Asqrt%2830%29  |multiplying numerator and denominator by sqrt%285%29