What is 2/((x-3))-3/((x+2))<(12)/((x^2-x-6)) ?

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

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2/((x-3))-3/((x+2))<(12)/((x^2-x-6))

\frac{2}{( x - 3 )} - \frac{3}{( x + 2 )} < \frac{12}{( x ^{2} - x - 6 )}

- 2 < x < 1 or x > 3

Interval Notation

(- 2, 1) \cup (3, \infty)

Solution steps

\frac{2}{x - 3} - \frac{3}{x + 2} < \frac{12}{x ^{2} - x - 6}

Rewrite in standard form

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

Identify the intervals

- 2 < x < 1 or x > 3

\frac{( 5 [ x ] + 4 )}{( 11 [ x ] + 7 )} \geq 3

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

x^{2} > \frac{4}{13}

\frac{( ( x + 5 ) ( x - 8 ) )}{( x - 12 )} > 0

7 x + 5 x < x^{2} - 10

What is 2/((x-3))-3/((x+2))<(12)/((x^2-x-6)) ?
The solution to 2/((x-3))-3/((x+2))<(12)/((x^2-x-6)) is -2<x<1\lor x>3