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

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

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

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

0 < x < 1 or 1 < x < 3

Interval Notation

(0, 1) \cup (1, 3)

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x - 3 ) ) ( - 1 )}{( x - 1 ) ^{2}} < 0 \cdot (- 1)

Simplify

\frac{x ( x - 3 )}{( x - 1 ) ^{2}} < 0

Identify the intervals

0 < x < 1 or 1 < x < 3

x (x + 6) (x + 2)^{2} (x - 3) > 0

x^{2} + 4 x + 6 > 0

\frac{( ( x - 1 ) ( 3 - x ) )}{( x ^{2} - 5 x )} > 0

2 x^{2} - 3 x + 5 < 0

\frac{( x - 2 ) ^{2} \cdot ( x ^{2} - 3 )}{( ( x + 1 ) ^{3} )} < 0

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