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

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

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

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

x < - 2 - 2 or - 3 < x < - 2 + 2

Interval Notation

(- \infty, - 2 - 2) \cup (- 3, - 2 + 2)

Decimal Notation

x < - 3.41421 \dots or - 3 < x < - 0.58578 \dots

Solution steps

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

Rewrite in standard form

\frac{- x ^{2} - 4 x - 2}{x + 3} > 0

Factor

- x^{2} - 4 x - 2 : - (x + 2 - 2) (x + 2 + 2)

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < - 2 - 2 or - 3 < x < - 2 + 2

4 ∣ 3 a + 4 ∣ = 16 a + 8

\frac{1}{4} x = 3

∣ 1 - x ∣ > 2

- \frac{x}{4} + \frac{9}{2} = \frac{2}{3} x - 1

\frac{e ^{7 i} - e ^{- 7 i}}{2 i}

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