What is ((3x-x^2))/(((x+4)^2))>= 0 ?

The solution to ((3x-x^2))/(((x+4)^2))>= 0 is 0<= x<= 3

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((3x-x^2))/(((x+4)^2))>= 0

\frac{( 3 x - x ^{2} )}{( ( x + 4 ) ^{2} )} \geq 0

0 \leq x \leq 3

Interval Notation

[0, 3]

Solution steps

\frac{3 x - x ^{2}}{( x + 4 ) ^{2}} \geq 0

Factor

\frac{3 x - x ^{2}}{( x + 4 ) ^{2}} : \frac{- x ( x - 3 )}{( x + 4 ) ^{2}}

\frac{- x ( x - 3 )}{( x + 4 ) ^{2}} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x - 3 ) ) ( - 1 )}{( x + 4 ) ^{2}} \leq 0 \cdot (- 1)

Simplify

\frac{x ( x - 3 )}{( x + 4 ) ^{2}} \leq 0

Identify the intervals

0 \leq x \leq 3

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

\frac{( x + 5 )}{( x + 1 )} > 0

\frac{1}{( 2 x - 7 )} \geq 0

\frac{( x ^{2} - 5 x )}{( x + 2 )} \geq 0

\frac{( 2 x + 3 )}{( 3 x - 7 )} \geq 1

What is ((3x-x^2))/(((x+4)^2))>= 0 ?
The solution to ((3x-x^2))/(((x+4)^2))>= 0 is 0<= x<= 3