How do you solve #\frac { 7} { x + 1} + \frac { x } { x ^ { 2} - 1} = \frac { 1} { x - 1}#?

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Answer 1 · 2017-08-28T05:16:14

#x=8/7#

First, we can eliminate the denominators. If you notice the denominators, the one denominator (the middle) is the product of the other two.

#(x+1)(x-1)=x^2-1#

So, we can multiply through by #(x+1)(x-1)#.

#7/(x+1)+x/(x^2-1)=1/(x-1) ->#

#(x+1)(x-1)(7/(x+1)+x/(x^2-1)=1/(x-1)) ->#

#7(x-1)+x=x+1#

Then, we can solve for x.

#7(x-1)+x=x+1 ->#

#8x-7=x+1 ->#

#7x=8#

#x=8/7#

If you want, you can plug this answer in to check if it is correct.