What is x/(x+1)>= 2/x ?

The solution to x/(x+1)>= 2/x is x = 1+sqrt(3)

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x/(x+1)>= 2/x

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

x < - 1 or 1 - 3 \leq x < 0 or x \geq 1 + 3

Interval Notation

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

Decimal Notation

x < - 1 or - 0.73205 \dots \leq x < 0 or x \geq 2.73205 \dots

Solution steps

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

Rewrite in standard form

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

Identify the intervals

x < - 1 or 1 - 3 \leq x < 0 or x \geq 1 + 3

4 y^{2} + 25 y + 6

- \frac{7}{2} + 7

20 x^{2} - 39 x + 80 = 0

\frac{1}{2} (x - 3) - \frac{3}{5} (2 x - 5) = 3 - \frac{3}{4} (2 x - 6)

x^{2} - 3 x + 2 \geq 0

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