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Question 427560: I need help solving this?
4/(x-1)+1=8/(x^2-1)
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website! I need help solving this?
4/(x-1) + 1 = 8 /(x^2 - 1)
4 / (x - 1) + 1 = 8 / (x + 1)(x - 1) {factored x^2 - 1 into two binomials on right side}
(x + 1)(x - 1)[4/(x - 1)] + (x + 1)(x - 1)(1) = (x + 1)(x - 1)[8/(x + 1)(x - 1)] {multiplied each term by LCD: (x + 1)(x - 1)
4(x + 1) + x^2 - 1 = 8 {cancelled and multiplied what's left}
4x + 4 + x^2 - 1 = 8 {used distributive property}
x^2 + 4x + 3 = 8 {combined like terms on left side}
x^2 + 4x - 5 = 0 {subtracted 8 from both sides}
(x + 5)(x - 1) = 0 {factored into two binomials}
x + 5 = 0 or x - 1 = 0 {set each factor equal to 0}
x = - 5 or x = 1 {solved each equation for x}
x = -5
x cannot be 1, it is an "extraneous solution".
If you put 1 back in, it makes one of the denominators 0, which is impossible.
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