What is ((sqrt(x)-1))/((sqrt(x)+1))>0 ?

The solution to ((sqrt(x)-1))/((sqrt(x)+1))>0 is x>1

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((sqrt(x)-1))/((sqrt(x)+1))>0

\frac{( x - 1 )}{( x + 1 )} > 0

x > 1

Interval Notation

(1, \infty)

Solution steps

\frac{x - 1}{x + 1} > 0

Let

u = x

\frac{u - 1}{u + 1} > 0

\frac{u - 1}{u + 1} > 0 : u < - 1 or u > 1

u < - 1 or u > 1

Substitute back

u = x

x < - 1 or x > 1

x < - 1 :

No Solution for

x \in R

x > 1 : x > 1

Combine the intervals

No Solution or x > 1

Merge Overlapping Intervals

x > 1

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

x > 1 and x \geq 0

Merge Overlapping Intervals

x > 1

x - 1 > 3 - x

x^{2} - 5 x + 4 \leq 2 x - 2

2 x - 3 - x - 2 > 2

(x - 8)^{\frac{1}{2}} \geq 12 - x

2 x < x^{2}

What is ((sqrt(x)-1))/((sqrt(x)+1))>0 ?
The solution to ((sqrt(x)-1))/((sqrt(x)+1))>0 is x>1