What is 3/(x^2-1)+1> 2/(x-1) ?

The solution to 3/(x^2-1)+1> 2/(x-1) is x 2

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3/(x^2-1)+1> 2/(x-1)

\frac{3}{x ^{2} - 1} + 1 > \frac{2}{x - 1}

x < - 1 or 0 < x < 1 or x > 2

Interval Notation

(- \infty, - 1) \cup (0, 1) \cup (2, \infty)

Solution steps

\frac{3}{x ^{2} - 1} + 1 > \frac{2}{x - 1}

Rewrite in standard form

\frac{x ^{2} - 2 x}{( x + 1 ) ( x - 1 )} > 0

Factor

\frac{x ^{2} - 2 x}{( x + 1 ) ( x - 1 )} : \frac{x ( x - 2 )}{( x + 1 ) ( x - 1 )}

\frac{x ( x - 2 )}{( x + 1 ) ( x - 1 )} > 0

Identify the intervals

x < - 1 or 0 < x < 1 or x > 2

6 - 3 + 4 x + 1 = 5 x + 7

- x + 8 > 6

3 x^{2} + 8 x \leq 0

4 x^{2} - 12 x + 25 = 0

4 x^{2} - 18 x + 20 = 0

What is 3/(x^2-1)+1> 2/(x-1) ?
The solution to 3/(x^2-1)+1> 2/(x-1) is x<-1\lor 0<x<1\lor x>2