What is 1/((x+1))+2/((x+3))> 3/((x+2)) ?

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

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1/((x+1))+2/((x+3))> 3/((x+2))

\frac{1}{( x + 1 )} + \frac{2}{( x + 3 )} > \frac{3}{( x + 2 )}

- 3 < x < - 2 or - 1 < x < 1

Interval Notation

(- 3, - 2) \cup (- 1, 1)

Solution steps

\frac{1}{x + 1} + \frac{2}{x + 3} > \frac{3}{x + 2}

Rewrite in standard form

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

Identify the intervals

- 3 < x < - 2 or - 1 < x < 1

\frac{- 4}{( 2 + 5 x )} < 0

(x + 5) (2 x - 3)^{5} (x - 7)^{3} (3 x + 8)^{2} < 0

6 x^{2} - 2 x + 3 > 0

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

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

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