What is 8/(x-3)+8/(x+1)<-3 ?

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

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8/(x-3)+8/(x+1)<-3

\frac{8}{x - 3} + \frac{8}{x + 1} < - 3

- 5 < x < - 1 or \frac{5}{3} < x < 3

Solution steps

\frac{8}{x - 3} + \frac{8}{x + 1} < - 3

Rewrite in standard form

\frac{3 x ^{2} + 10 x - 25}{( x - 3 ) ( x + 1 )} < 0

Factor

\frac{3 x ^{2} + 10 x - 25}{( x - 3 ) ( x + 1 )} : \frac{( 3 x - 5 ) ( x + 5 )}{( x - 3 ) ( x + 1 )}

\frac{( 3 x - 5 ) ( x + 5 )}{( x - 3 ) ( x + 1 )} < 0

Identify the intervals

- 5 < x < - 1 or \frac{5}{3} < x < 3

2 (2 x + 1)^{2} - 2 = 160

x^{2} + 4 x + 21 = 0

\frac{2}{10}

- \frac{8 + r}{2} > - 8

(5 x - 3)^{2} = 25

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