What is ((x^2-1))/((2x+5))<3 ?

The solution to ((x^2-1))/((2x+5))<3 is x<-5/2 \lor-2<x<8

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((x^2-1))/((2x+5))<3

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

x < - \frac{5}{2} or - 2 < x < 8

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- 2, 8)

Decimal Notation

x < - 2.5 or - 2 < x < 8

Solution steps

\frac{x ^{2} - 1}{2 x + 5} < 3

Rewrite in standard form

\frac{x ^{2} - 6 x - 16}{2 x + 5} < 0

Factor

\frac{x ^{2} - 6 x - 16}{2 x + 5} : \frac{( x + 2 ) ( x - 8 )}{2 x + 5}

\frac{( x + 2 ) ( x - 8 )}{2 x + 5} < 0

Identify the intervals

x < - \frac{5}{2} or - 2 < x < 8

- x^{2} - 4 x - 5 < 0

\frac{( 2 x - 1 ) ( x - 1 ) ^{2} ( x - 2 ) ^{3}}{( x - 4 )} > 0

\frac{( [ x ] - 2 )}{( 4 - [ x ] )} > 0

x^{3} - x > 2 x^{2} - 2

9 x^{2} - 4 < 0

What is ((x^2-1))/((2x+5))<3 ?
The solution to ((x^2-1))/((2x+5))<3 is x<-5/2 \lor-2<x<8