What is (3x-12)/((x-2)(x-8))<0 ?

The solution to (3x-12)/((x-2)(x-8))<0 is x<2\lor 4<x<8

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(3x-12)/((x-2)(x-8))<0

\frac{3 x - 12}{( x - 2 ) ( x - 8 )} < 0

x < 2 or 4 < x < 8

Interval Notation

(- \infty, 2) \cup (4, 8)

Solution steps

\frac{3 x - 12}{( x - 2 ) ( x - 8 )} < 0

Factor

\frac{3 x - 12}{( x - 2 ) ( x - 8 )} : \frac{3 ( x - 4 )}{( x - 2 ) ( x - 8 )}

\frac{3 ( x - 4 )}{( x - 2 ) ( x - 8 )} < 0

Divide both sides by

3

\frac{\frac{3 ( x - 4 )}{( x - 2 ) ( x - 8 )}}{3} < \frac{0}{3}

Simplify

\frac{x - 4}{( x - 2 ) ( x - 8 )} < 0

Identify the intervals

x < 2 or 4 < x < 8

8 x - (6 x - 9) + (3 x - 2) = 4 - (7 x - 8)

- 3 v + 11 = - 8 v + 51

- \frac{1}{2} (x + 5) = - 10

x^{2} + 13 x + 5 = 0

\frac{1}{6} < \frac{2 x - 11}{12} \leq \frac{2}{3}

What is (3x-12)/((x-2)(x-8))<0 ?
The solution to (3x-12)/((x-2)(x-8))<0 is x<2\lor 4<x<8