What is ((x^2+7x+10))/((x^2-4))>= 0 ?

The solution to ((x^2+7x+10))/((x^2-4))>= 0 is x 2

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((x^2+7x+10))/((x^2-4))>= 0

\frac{( x ^{2} + 7 x + 10 )}{( x ^{2} - 4 )} \geq 0

x \leq - 5 or x > 2

Interval Notation

(- \infty, - 5] \cup (2, \infty)

Solution steps

\frac{x ^{2} + 7 x + 10}{x ^{2} - 4} \geq 0

Factor

\frac{x ^{2} + 7 x + 10}{x ^{2} - 4} : \frac{( x + 2 ) ( x + 5 )}{( x + 2 ) ( x - 2 )}

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

Identify the intervals

x \leq - 5 or x > 2

6 x^{3} + x^{2} - 54 x + 56 < 0

\frac{x}{( x - 3 )} < \frac{9}{( 4 x + 3 )}

\frac{( x - 4 )}{( x + 2 )} \geq \frac{( x - 5 )}{( x + 4 )}

x^{3} + 9 x^{2} \leq - 26 x - 24

x, f < - 8

What is ((x^2+7x+10))/((x^2-4))>= 0 ?
The solution to ((x^2+7x+10))/((x^2-4))>= 0 is x<=-5\lor x>2