What is (2x+5)/(x+1)>(x+1)/(x-1) ?

The solution to (2x+5)/(x+1)>(x+1)/(x-1) is x 2

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(2x+5)/(x+1)>(x+1)/(x-1)

\frac{2 x + 5}{x + 1} > \frac{x + 1}{x - 1}

x < - 3 or - 1 < x < 1 or x > 2

Interval Notation

(- \infty, - 3) \cup (- 1, 1) \cup (2, \infty)

Solution steps

\frac{2 x + 5}{x + 1} > \frac{x + 1}{x - 1}

Rewrite in standard form

\frac{x ^{2} + x - 6}{( x + 1 ) ( x - 1 )} > 0

Factor

\frac{x ^{2} + x - 6}{( x + 1 ) ( x - 1 )} : \frac{( x - 2 ) ( x + 3 )}{( x + 1 ) ( x - 1 )}

\frac{( x - 2 ) ( x + 3 )}{( x + 1 ) ( x - 1 )} > 0

Identify the intervals

x < - 3 or - 1 < x < 1 or x > 2

7 x y - 21 x z

∣ 4 x - 2 ∣ \geq x + 1

4 x - 3 < 5

\frac{- 9 a ^{5} b ^{8}}{3 a ^{2} b ^{4}}

What is (2x+5)/(x+1)>(x+1)/(x-1) ?
The solution to (2x+5)/(x+1)>(x+1)/(x-1) is x<-3\lor-1<x<1\lor x>2