What is 1/x+1/(x+1)< 2/(x+4) ?

The solution to 1/x+1/(x+1)< 2/(x+4) is -4<x<-1\lor-4/7 <x<0

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1/x+1/(x+1)< 2/(x+4)

\frac{1}{x} + \frac{1}{x + 1} < \frac{2}{x + 4}

- 4 < x < - 1 or - \frac{4}{7} < x < 0

Interval Notation

(- 4, - 1) \cup (- \frac{4}{7}, 0)

Decimal Notation

- 4 < x < - 1 or - 0.57142 \dots < x < 0

Solution steps

\frac{1}{x} + \frac{1}{x + 1} < \frac{2}{x + 4}

Rewrite in standard form

\frac{7 x + 4}{x ( x + 1 ) ( x + 4 )} < 0

Identify the intervals

- 4 < x < - 1 or - \frac{4}{7} < x < 0

14 x^{2} - x - 3

10 x - 2 - 7 x = 16

3.5 + 2.5 x = 9.75

\frac{3 x}{5} - \frac{2 x}{3} + \frac{1}{5} = 0

4 (2 x + 5) = 3 (x + 15)

What is 1/x+1/(x+1)< 2/(x+4) ?
The solution to 1/x+1/(x+1)< 2/(x+4) is -4<x<-1\lor-4/7 <x<0