What is (2x-12)/((x-2)(x-9))<0 ?

The solution to (2x-12)/((x-2)(x-9))<0 is x<2\lor 6<x<9

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(2x-12)/((x-2)(x-9))<0

\frac{2 x - 12}{( x - 2 ) ( x - 9 )} < 0

x < 2 or 6 < x < 9

Interval Notation

(- \infty, 2) \cup (6, 9)

Solution steps

\frac{2 x - 12}{( x - 2 ) ( x - 9 )} < 0

Factor

\frac{2 x - 12}{( x - 2 ) ( x - 9 )} : \frac{2 ( x - 6 )}{( x - 2 ) ( x - 9 )}

\frac{2 ( x - 6 )}{( x - 2 ) ( x - 9 )} < 0

Divide both sides by

2

\frac{\frac{2 ( x - 6 )}{( x - 2 ) ( x - 9 )}}{2} < \frac{0}{2}

Simplify

\frac{x - 6}{( x - 2 ) ( x - 9 )} < 0

Identify the intervals

x < 2 or 6 < x < 9

- (\frac{1}{5})^{- 2}

x (x - 5) \geq 0

x^{2} + 2 x - 120

(\frac{2}{5}) x = 4 x - 12

x^{4} - 4 x^{2}

What is (2x-12)/((x-2)(x-9))<0 ?
The solution to (2x-12)/((x-2)(x-9))<0 is x<2\lor 6<x<9