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

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

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

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

x < - 3 or - 3 < x \leq - 2 or x > 2

Interval Notation

(- \infty, - 3) \cup (- 3, - 2] \cup (2, \infty)

Solution steps

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

Factor

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

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

Identify the intervals

x < - 3 or - 3 < x \leq - 2 or x > 2

7 x^{- 3} \cdot 4 x^{- 2}

- \frac{4 x}{5} < 0

(y + 10 - 3)^{2} + y^{2} = 49

\frac{4 - ( \frac{3}{4} ) ^{2}}{2 ( \frac{3}{4} )}

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