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

The solution to (x-1)/(x+1)-x/(x-2)>1 is -4<x<-1\lor 1<x<2

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

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

- 4 < x < - 1 or 1 < x < 2

Interval Notation

(- 4, - 1) \cup (1, 2)

Solution steps

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

Rewrite in standard form

\frac{- x ^{2} - 3 x + 4}{( x + 1 ) ( x - 2 )} > 0

Factor

\frac{- x ^{2} - 3 x + 4}{( x + 1 ) ( x - 2 )} : \frac{- ( x - 1 ) ( x + 4 )}{( x + 1 ) ( x - 2 )}

\frac{- ( x - 1 ) ( x + 4 )}{( x + 1 ) ( x - 2 )} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 1 ) ( x + 4 ) ) ( - 1 )}{( x + 1 ) ( x - 2 )} < 0 \cdot (- 1)

Simplify

\frac{( x - 1 ) ( x + 4 )}{( x + 1 ) ( x - 2 )} < 0

Identify the intervals

- 4 < x < - 1 or 1 < x < 2

36000 = \frac{2 ( 9 \cdot 1 0 ^{9} ) ( \frac{x}{2.46} )}{0.217}

- 3 = x^{2} + 5 x

9 (9 t - 4) \geq 12 (12 t - 3)

40 = 490 t^{2}

\frac{y}{4} = \frac{3}{6}

What is (x-1)/(x+1)-x/(x-2)>1 ?
The solution to (x-1)/(x+1)-x/(x-2)>1 is -4<x<-1\lor 1<x<2