What is (4x+6)/(x^2+5x+6)>= 1 ?

The solution to (4x+6)/(x^2+5x+6)>= 1 is -3<x<-2\lor-1<= x<= 0

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(4x+6)/(x^2+5x+6)>= 1

\frac{4 x + 6}{x ^{2} + 5 x + 6} \geq 1

- 3 < x < - 2 or - 1 \leq x \leq 0

Interval Notation

(- 3, - 2) \cup [- 1, 0]

Solution steps

\frac{4 x + 6}{x ^{2} + 5 x + 6} \geq 1

Rewrite in standard form

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

Factor

\frac{- x ^{2} - x}{x ^{2} + 5 x + 6} : \frac{- x ( x + 1 )}{( x + 2 ) ( x + 3 )}

\frac{- x ( x + 1 )}{( x + 2 ) ( x + 3 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x + 1 ) ) ( - 1 )}{( x + 2 ) ( x + 3 )} \leq 0 \cdot (- 1)

Simplify

\frac{x ( x + 1 )}{( x + 2 ) ( x + 3 )} \leq 0

Identify the intervals

- 3 < x < - 2 or - 1 \leq x \leq 0

\frac{4}{3} - \frac{2}{4}

9 y - 6 + y + 8 = 42

(x - 4) (x - 3) < 6

8 a^{2} - 72 = 0

6 \cdot 46

What is (4x+6)/(x^2+5x+6)>= 1 ?
The solution to (4x+6)/(x^2+5x+6)>= 1 is -3<x<-2\lor-1<= x<= 0