What is sqrt(x+2)< x/(x+2) ?

The solution to sqrt(x+2)< x/(x+2) is No Solution for x\in\mathbb{R}

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sqrt(x+2)< x/(x+2)

x + 2 < \frac{x}{x + 2}

No Solution for x \in R

Solution steps

x + 2 < \frac{x}{x + 2}

f (x) < g (x)

then

g (x) > 0

\frac{x}{x + 2} > 0 : x < - 2 or x > 0

x + 2 < \frac{x}{x + 2} : x < - 2 or - 2 < x < - 1

Find singularity points

Find non-negative values for radicals:

x \geq - 2

Combine the intervals

(x < - 2 or x > 0) and (x < - 2 or - 2 < x < - 1) and x \geq - 2

Merge Overlapping Intervals

No Solution for x \in R

8 a^{2} + 16 b^{2}

276 + 7150

- 5 \leq 2 a - 1 < 9

7 x + 3 = x - 3

\frac{3 y ^{2}}{2} - \frac{y}{4} = \frac{y}{2}

What is sqrt(x+2)< x/(x+2) ?
The solution to sqrt(x+2)< x/(x+2) is No Solution for x\in\mathbb{R}