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

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

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

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

0 < x \leq \frac{5 - 21}{2} or x > 1

Interval Notation

(0, \frac{5 - 21}{2}] \cup (1, \infty)

Decimal Notation

0 < x \leq 0.20871 \dots or x > 1

Solution steps

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

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

No Solution or 0 < x \leq \frac{5 - 21}{2} or x > 1

Merge Overlapping Intervals

0 < x \leq \frac{5 - 21}{2} or x > 1

(\frac{3 ( x - 12 ) ^{\frac{1}{2}}}{2})^{2}

3 x^{2} + 9 x - 4 = 0

1 + x^{2} = 0

2 x^{3} + 17 x^{2} + 46 x + 40

\frac{3 x - 7 ( x + 1 )}{6} = \frac{2 x - 1}{3} - 2

What is (|x-1|)/x+(x+2)/(x-1)>= 1 ?
The solution to (|x-1|)/x+(x+2)/(x-1)>= 1 is 0<x<= (5-sqrt(21))/2 \lor x>1