What is (x+2)/(x+3)-(x-1)/(x-2)<0 ?

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

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(x+2)/(x+3)-(x-1)/(x-2)<0

\frac{x + 2}{x + 3} - \frac{x - 1}{x - 2} < 0

- 3 < x < - \frac{1}{2} or x > 2

Interval Notation

(- 3, - \frac{1}{2}) \cup (2, \infty)

Decimal Notation

- 3 < x < - 0.5 or x > 2

Solution steps

\frac{x + 2}{x + 3} - \frac{x - 1}{x - 2} < 0

Rewrite in standard form

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

Identify the intervals

- 3 < x < - \frac{1}{2} or x > 2

∣ x - 4 ∣ < 0

4 x^{2} = - 32 x

\frac{π}{6} \cdot 2

5 = \frac{4 x + 23}{3}

x = \frac{26}{10} - \frac{8}{10} (- 3)

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