What is (2x-10)/((x-2)(x-8))<0 ?

The solution to (2x-10)/((x-2)(x-8))<0 is x<2\lor 5<x<8

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(2x-10)/((x-2)(x-8))<0

\frac{2 x - 10}{( x - 2 ) ( x - 8 )} < 0

x < 2 or 5 < x < 8

Interval Notation

(- \infty, 2) \cup (5, 8)

Solution steps

\frac{2 x - 10}{( x - 2 ) ( x - 8 )} < 0

Factor

\frac{2 x - 10}{( x - 2 ) ( x - 8 )} : \frac{2 ( x - 5 )}{( x - 2 ) ( x - 8 )}

\frac{2 ( x - 5 )}{( x - 2 ) ( x - 8 )} < 0

Divide both sides by

2

\frac{\frac{2 ( x - 5 )}{( x - 2 ) ( x - 8 )}}{2} < \frac{0}{2}

Simplify

\frac{x - 5}{( x - 2 ) ( x - 8 )} < 0

Identify the intervals

x < 2 or 5 < x < 8

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What is (2x-10)/((x-2)(x-8))<0 ?
The solution to (2x-10)/((x-2)(x-8))<0 is x<2\lor 5<x<8