What is (|sqrt(x+5)|)/(|1-x|)>1 ?

The solution to (|sqrt(x+5)|)/(|1-x|)>1 is -1<x<1\lor 1<x<4

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(|sqrt(x+5)|)/(|1-x|)>1

\frac{x + 5}{∣ 1 - x ∣} > 1

- 1 < x < 1 or 1 < x < 4

Solution steps

\frac{x + 5}{∣ 1 - x ∣} > 1

Apply absolute rule: if

n

is even,

u > 0

then

x + 5 = x + 5

\frac{x + 5}{∣ 1 - x ∣} > 1

Find positive and negative intervals

x \leq 1, x > 1

Solve the inequality for each interval

- 1 < x < 1 or 1 < x < 4

∣ 2 x - 10 ∣ > 10

∣ x ∣^{x^{2} - x - 2} < 1

∣ 5 x - 2 ∣ \leq ∣ 3 x + 5 ∣

∣ x + 3 ∣ > ∣ 2 x - 4 ∣

\frac{2}{( x + 3 )} \leq 1

What is (|sqrt(x+5)|)/(|1-x|)>1 ?
The solution to (|sqrt(x+5)|)/(|1-x|)>1 is -1<x<1\lor 1<x<4