What is (4x+5)/(x^2)>= 4/(x+5) ?

The solution to (4x+5)/(x^2)>= 4/(x+5) is x 0

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(4x+5)/(x^2)>= 4/(x+5)

\frac{4 x + 5}{x ^{2}} \geq \frac{4}{x + 5}

x < - 5 or - 1 \leq x < 0 or x > 0

Interval Notation

(- \infty, - 5) \cup [- 1, 0) \cup (0, \infty)

Solution steps

\frac{4 x + 5}{x ^{2}} \geq \frac{4}{x + 5}

Rewrite in standard form

\frac{25 x + 25}{x ^{2} ( x + 5 )} \geq 0

Factor

\frac{25 x + 25}{x ^{2} ( x + 5 )} : \frac{25 ( x + 1 )}{x ^{2} ( x + 5 )}

\frac{25 ( x + 1 )}{x ^{2} ( x + 5 )} \geq 0

Divide both sides by

25

\frac{\frac{25 ( x + 1 )}{x ^{2} ( x + 5 )}}{25} \geq \frac{0}{25}

Simplify

\frac{x + 1}{x ^{2} ( x + 5 )} \geq 0

Identify the intervals

x < - 5 or - 1 \leq x < 0 or x > 0

\frac{3}{4} = \frac{y}{8}

2 p \geq 14

7 x^{2} - 7 x + 3 = 0

x + 6 < 5

7 ∣ 8 - 3 h ∣ = 21 h - 49

What is (4x+5)/(x^2)>= 4/(x+5) ?
The solution to (4x+5)/(x^2)>= 4/(x+5) is x<-5\lor-1<= x<0\lor x>0