Question 452345
solve this rational equation. {{{x/(x+1) + 5/(x-1)}}} = 1
:
Multiply each term by (x+1)(x-1)
:
(x+1)(x-1)*{{{x/(x+1)}}} + (x-1)(x+1)*{{{5/(x-1)}}} = (x-1)(x+1)*1
:
Cancel the denominators and you are left with
(x-1)*x + (x+1)*5 = (x+1)(x-1)
then
x^2 - x + 5x + 5 = x^2 - x + x - 1
x^2 + 4x + 5 = x^2 - 1
Combine the x^2 on the left, number on the right
x^2 - x^2 + 4x = - 1 - 5
4x = -6
x = {{{(-6)/4}}}
x = -1.5
:
:
see if that works in the original problem
{{{(-1.5)/(-1.5+1) + 5/(-1.5-1)}}} = 1
{{{(-1.5)/(-.5) + 5/(-2.5)}}} = 1
+3 - 2 = 1