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

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

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

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

x < 2 or 4 < x < 8

Interval Notation

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

Solution steps

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

Factor

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

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x < 2 or 4 < x < 8

2 lo g_{10} (5) + lo g_{10} (4)

\frac{1}{2} x^{2} + \frac{1}{10} x - 1 = 0

\frac{( \frac{7}{3} \cdot 9 - 18 \cdot ( \frac{1}{3} ) ^{2} )}{4 + \frac{7}{3}}

36 x^{2} - 12 x + 1 = 0

3 x + 4 > 10

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