What is (1(5x+1))/(((x+1)^2))<1 ?

The solution to (1(5x+1))/(((x+1)^2)) 3

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(1(5x+1))/(((x+1)^2))<1

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

x < - 1 or - 1 < x < 0 or x > 3

Interval Notation

(- \infty, - 1) \cup (- 1, 0) \cup (3, \infty)

Solution steps

\frac{1 \cdot ( 5 x + 1 )}{( x + 1 ) ^{2}} < 1

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < - 1 or - 1 < x < 0 or x > 3

(1 - 0.25 \cdot x) \cdot (20 + x) > 20

x^{2} - x + 1 \geq 0

\frac{3}{2 x - 1} < - 2

x (x - 10) < - 2 x - 7

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

What is (1(5x+1))/(((x+1)^2))<1 ?
The solution to (1(5x+1))/(((x+1)^2))<1 is x<-1\lor-1<x<0\lor x>3