SOLUTION: 1/(x+1) + a/(x^2-1) = x/(x^2-1) to hold for all x, a must equal a # simplify the left side of the equation and compare what you get with the right side. (1/(x+1))(x^2-1)/(x^2-

Question 511788: 1/(x+1) + a/(x^2-1) = x/(x^2-1) to hold for all x, a must equal a #
simplify the left side of the equation and compare what you get with the right side.
(1/(x+1))(x^2-1)/(x^2-1) + (a/(x^2-1))(x+1)/(x+1)= (x^2-1)+a(x+1)/((x^2-1)(x+1))
therefore (ax+a)/(x^3-x) which simplifies to a/(x(x-1))
but this is not a number... let me know! thanks!
Answer by John10(297) (Show Source): You can put this solution on YOUR website!
Okay.. your equation is like below:
1/(x + 1) + a/(x^2 - 1) = x/(x^2 - 1)
You know that the LCD is x^2 - 1 = (x - 1)(x + 1)
You multiply both sides by LCD and simplify, you will have the below statement:
1(x - 1) + a = x
x - 1 + a =x
Subtract x from both sides:
x - x - 1 + a = x - x
-1 + a = 0
a = 1 which is what you are looking for.
John10:)
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