What is ((x^2+6x-11))/((x+3))<-1 ?

The solution to ((x^2+6x-11))/((x+3))<-1 is x<-8\lor-3<x<1

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((x^2+6x-11))/((x+3))<-1

\frac{( x ^{2} + 6 x - 11 )}{( x + 3 )} < - 1

x < - 8 or - 3 < x < 1

Interval Notation

(- \infty, - 8) \cup (- 3, 1)

Solution steps

\frac{x ^{2} + 6 x - 11}{x + 3} < - 1

Rewrite in standard form

\frac{x ^{2} + 7 x - 8}{x + 3} < 0

Factor

\frac{x ^{2} + 7 x - 8}{x + 3} : \frac{( x - 1 ) ( x + 8 )}{x + 3}

\frac{( x - 1 ) ( x + 8 )}{x + 3} < 0

Identify the intervals

x < - 8 or - 3 < x < 1

(4 x - 5)^{2} - 16 x (x + 3) < - 21

\frac{( 2 x + 1 )}{( x ^{2} - x - 12 )} \leq \frac{1}{2}

(x + 9) (x - 3) > 0

(x - 1)^{2} - 11 < (x - 2)^{2}

4 x^{2} + 2 > 0

What is ((x^2+6x-11))/((x+3))<-1 ?
The solution to ((x^2+6x-11))/((x+3))<-1 is x<-8\lor-3<x<1