What is 1/(x-3)+4/(x-8)>= 0 ?

The solution to 1/(x-3)+4/(x-8)>= 0 is 3 8

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1/(x-3)+4/(x-8)>= 0

\frac{1}{x - 3} + \frac{4}{x - 8} \geq 0

3 < x \leq 4 or x > 8

Interval Notation

(3, 4] \cup (8, \infty)

Solution steps

\frac{1}{x - 3} + \frac{4}{x - 8} \geq 0

Rewrite in standard form

\frac{5 x - 20}{( x - 3 ) ( x - 8 )} \geq 0

Factor

\frac{5 x - 20}{( x - 3 ) ( x - 8 )} : \frac{5 ( x - 4 )}{( x - 3 ) ( x - 8 )}

\frac{5 ( x - 4 )}{( x - 3 ) ( x - 8 )} \geq 0

Divide both sides by

5

\frac{\frac{5 ( x - 4 )}{( x - 3 ) ( x - 8 )}}{5} \geq \frac{0}{5}

Simplify

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

Identify the intervals

3 < x \leq 4 or x > 8

\frac{4}{49}

3 > \frac{n}{2}

122 = - 2 (7 x - 5)

125 x^{3} - 1

\frac{3 + 7 i}{1 + i}

What is 1/(x-3)+4/(x-8)>= 0 ?
The solution to 1/(x-3)+4/(x-8)>= 0 is 3<x<= 4\lor x>8