What is ((2x+10))/((x^2-5x+6))>= 0 ?

The solution to ((2x+10))/((x^2-5x+6))>= 0 is -5 3

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((2x+10))/((x^2-5x+6))>= 0

\frac{( 2 x + 10 )}{( x ^{2} - 5 x + 6 )} \geq 0

- 5 \leq x < 2 or x > 3

Interval Notation

[- 5, 2) \cup (3, \infty)

Solution steps

\frac{2 x + 10}{x ^{2} - 5 x + 6} \geq 0

Factor

\frac{2 x + 10}{x ^{2} - 5 x + 6} : \frac{2 ( x + 5 )}{( x - 2 ) ( x - 3 )}

\frac{2 ( x + 5 )}{( x - 2 ) ( x - 3 )} \geq 0

Divide both sides by

2

\frac{\frac{2 ( x + 5 )}{( x - 2 ) ( x - 3 )}}{2} \geq \frac{0}{2}

Simplify

\frac{x + 5}{( x - 2 ) ( x - 3 )} \geq 0

Identify the intervals

- 5 \leq x < 2 or x > 3

\frac{0}{- 5}

x^{2} - 17 x + 13 = - 27

- \frac{1}{2} \cdot 8

(4 a + \frac{1}{8} b)^{2}

3 x + 2 \leq 14

What is ((2x+10))/((x^2-5x+6))>= 0 ?
The solution to ((2x+10))/((x^2-5x+6))>= 0 is -5<= x<2\lor x>3