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

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

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

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

x < 0 or x > 3

Interval Notation

(- \infty, 0) \cup (3, \infty)

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

x < 0 or x > 3

x^{2} - 6 > 2

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

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

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

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

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