What is (((x-x^2))/((x^2+2x)))>= 0 ?

The solution to (((x-x^2))/((x^2+2x)))>= 0 is -2<x<= 1

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(((x-x^2))/((x^2+2x)))>= 0

(\frac{( x - x ^{2} )}{( x ^{2} + 2 x )}) \geq 0

- 2 < x \leq 1

Interval Notation

(- 2, 1]

Solution steps

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

\frac{x - 1}{x + 2} \leq 0

Identify the intervals

- 2 < x \leq 1

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

x (2 x + 3) > 3 x^{2} + 5

x^{4} + 5 < 0

\frac{1}{x - 2} > 0

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

What is (((x-x^2))/((x^2+2x)))>= 0 ?
The solution to (((x-x^2))/((x^2+2x)))>= 0 is -2<x<= 1