SOLUTION: Can you please assist me with this equation
14/x^2 + 1/x-1 = 3/x+1 I believe you would mulpliply both sides by x +1 but am not sure exactly where I am going with this. I would
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Question 394345: Can you please assist me with this equation
14/x^2 + 1/x-1 = 3/x+1 I believe you would mulpliply both sides by x +1 but am not sure exactly where I am going with this. I would appreciate any help you can give me. Thank you.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You want to multiply both sides of the equation by 1 in the form of the lowest common denominator divided by itself.
Since the three denominators have no common factors, the lowest common denominator is simply the product of the three denominators.
\left(\frac{(x^2)(x\ -\ 1)(x\ +\ 1)}{(x^2)(x\ -\ 1)(x\ +\ 1)}\right)\ =\ \left(\frac{3}{x\ +\ 1}\right)\left(\frac{(x^2)(x\ -\ 1)(x\ +\ 1)}{(x^2)(x\ -\ 1)(x\ +\ 1)}\right))
(x\ +\ 1)\ +\ (x^2)(x\ +\ 1)}{(x^2)(x\ -\ 1)(x\ +\ 1)}\ =\ \frac{3(x^2)(x\ -\ 1)}{(x^2)(x\ -\ 1)(x\ +\ 1)})
Now distribute, expand, and collect like terms in the numerators (verification is left as an exercise for the student -- and you had better verify it for yourself as I can and do make mistakes):
(x\ -\ 1)(x\ +\ 1)}\ =\ 0)
Now just solve the cubic. It doesn't factor over the rationals, so you are going to either have to use the general solution of a cubic:
Check out:
Wikipedia Cubic Function
Or
Wolfram Mathworld Cubic Formula
But be prepared for much wailing, gnashing of teeth, and pulling of hair.
Or
Google any one of several cubic calculators.
John
My calculator said it, I believe it, that settles it
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