What is 4/(x+1)< 2/(x+3) ?

The solution to 4/(x+1)< 2/(x+3) is x<-5\lor-3<x<-1

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4/(x+1)< 2/(x+3)

\frac{4}{x + 1} < \frac{2}{x + 3}

x < - 5 or - 3 < x < - 1

Interval Notation

(- \infty, - 5) \cup (- 3, - 1)

Solution steps

\frac{4}{x + 1} < \frac{2}{x + 3}

Rewrite in standard form

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

Factor

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

\frac{2 ( x + 5 )}{( x + 1 ) ( x + 3 )} < 0

Divide both sides by

2

\frac{\frac{2 ( x + 5 )}{( x + 1 ) ( x + 3 )}}{2} < \frac{0}{2}

Simplify

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

Identify the intervals

x < - 5 or - 3 < x < - 1

x^{3} \geq 2 x^{2}

343 y^{3} - 216

3 y + 6 x

∣ 3 x + 2 ∣ = ∣ 4 x + 5 ∣

10 x^{2} - 5 x