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

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

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

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

- 1 < x < 2

Interval Notation

(- 1, 2)

Solution steps

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

Rewrite in standard form

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

\frac{1}{a} < 0

then

a < 0

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

Identify the intervals

- 1 < x < 2

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

(x + 2) (x + 2) > x (x - 4)

\frac{( x ^{2} - 4 x + 7 )}{( x ^{2} - 7 x + 12 )} < \frac{2}{3}

(x - 2) \cdot (x - 4) > 0

\frac{( 3 x - 1 )}{( x + 2 )} => 5