What is (-3)/(x^2+6x+8)>= x/(x^2+6x+8) ?

The solution to (-3)/(x^2+6x+8)>= x/(x^2+6x+8) is x<-4\lor-3<= x<-2

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(-3)/(x^2+6x+8)>= x/(x^2+6x+8)

\frac{- 3}{x ^{2} + 6 x + 8} \geq \frac{x}{x ^{2} + 6 x + 8}

x < - 4 or - 3 \leq x < - 2

Interval Notation

(- \infty, - 4) \cup [- 3, - 2)

Solution steps

\frac{- 3}{x ^{2} + 6 x + 8} \geq \frac{x}{x ^{2} + 6 x + 8}

Rewrite in standard form

\frac{- 3 - x}{x ^{2} + 6 x + 8} \geq 0

Factor

\frac{- 3 - x}{x ^{2} + 6 x + 8} : \frac{- 3 - x}{( x + 2 ) ( x + 4 )}

\frac{- 3 - x}{( x + 2 ) ( x + 4 )} \geq 0

Identify the intervals

x < - 4 or - 3 \leq x < - 2

4 x^{2} - 4 x - 15 = 0

x^{2} + 10 x = 2 x

\frac{f}{- 7} - 8 = 2

\frac{4}{3 + 6}

2 lo g_{2} (8)

What is (-3)/(x^2+6x+8)>= x/(x^2+6x+8) ?
The solution to (-3)/(x^2+6x+8)>= x/(x^2+6x+8) is x<-4\lor-3<= x<-2