What is x/(x+2)-2/(x-1)<0 ?

The solution to x/(x+2)-2/(x-1)<0 is -2<x<-1\lor 1<x<4

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x/(x+2)-2/(x-1)<0

\frac{x}{x + 2} - \frac{2}{x - 1} < 0

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

Interval Notation

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

Solution steps

\frac{x}{x + 2} - \frac{2}{x - 1} < 0

Rewrite in standard form

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

Factor

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

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

Identify the intervals

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

\frac{6 ^{- 3}}{6 ^{5}}

2 w^{2} - 26 w - 60

f = 30 e^{- 0.093}

4 x^{2} + 4 x - 48

5 x^{2} - 24 x - 5 = 0

What is x/(x+2)-2/(x-1)<0 ?
The solution to x/(x+2)-2/(x-1)<0 is -2<x<-1\lor 1<x<4