Solve for x

Question

 x         2           8

----  + ----    = ----

x-1     x²-1      x+1

 

Answer 1

In order to add fractions you have to change each fraction to the lowest common denominator.  The lowest common denominator is x² - 1.

 

(x+1/x+1)(x/x-1) + 2/(x²-1) = 8/(x+1) (x-1/x-1)

 

[(x² + x) +2]/(x² - 1) = (8x - 8)/(x² - 1)

 

x² + x + 2 = 8x - 8

x² - 7x + 10 = 0

 

resort to the Quadratic Formula

 

{-10 ± √[10² - 4(1)(10)]}/2(1) = x

[-10 ± √(100-40)]/2 = x

(-10 ± √60)/2 = x

(-10 ± 2√15)/2 = x

-5 ± √15 = x