What is 1/(x-2)+3/(4x-36)>= 0 ?

The solution to 1/(x-2)+3/(4x-36)>= 0 is 2 9

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1/(x-2)+3/(4x-36)>= 0

\frac{1}{x - 2} + \frac{3}{4 x - 36} \geq 0

2 < x \leq 6 or x > 9

Interval Notation

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

Solution steps

\frac{1}{x - 2} + \frac{3}{4 x - 36} \geq 0

Rewrite in standard form

\frac{7 x - 42}{( x - 2 ) ( x - 9 )} \geq 0

Factor

\frac{7 x - 42}{( x - 2 ) ( x - 9 )} : \frac{7 ( x - 6 )}{( x - 2 ) ( x - 9 )}

\frac{7 ( x - 6 )}{( x - 2 ) ( x - 9 )} \geq 0

Divide both sides by

7

\frac{\frac{7 ( x - 6 )}{( x - 2 ) ( x - 9 )}}{7} \geq \frac{0}{7}

Simplify

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

Identify the intervals

2 < x \leq 6 or x > 9

p^{2} - 2 p - 15

7 x^{2} - 42 x = 0

7 x^{2} = - x

x^{2} + 3 x - 1 = 3

3 y^{2} + 19 y + 6

What is 1/(x-2)+3/(4x-36)>= 0 ?
The solution to 1/(x-2)+3/(4x-36)>= 0 is 2<x<= 6\lor x>9