What is (-(sqrt(x)+6))/((sqrt(x)-2))<3 ?

The solution to (-(sqrt(x)+6))/((sqrt(x)-2)) 4

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(-(sqrt(x)+6))/((sqrt(x)-2))<3

\frac{- ( x + 6 )}{( x - 2 )} < 3

x > 4

Interval Notation

(4, \infty)

Solution steps

\frac{- ( x + 6 )}{x - 2} < 3

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

\frac{x + 6}{x - 2} > - 3

Let

u = x

\frac{u + 6}{u - 2} > - 3

\frac{u + 6}{u - 2} > - 3 : u < 0 or u > 2

u < 0 or u > 2

Substitute back

u = x

x < 0 or x > 2

x < 0 :

No Solution for

x \in R

x > 2 : x > 4

Combine the intervals

No Solution or x > 4

Merge Overlapping Intervals

x > 4

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

x > 4 and x \geq 0

Merge Overlapping Intervals

x > 4

x + 4 x - 4 \geq 0

x^{2} + 3 x + 3 < 2 x + 1

x \geq 4 - x

(3) x + 3 + x^{2} + 4 x - 5 > 0

x + 2 < x + 5

What is (-(sqrt(x)+6))/((sqrt(x)-2))<3 ?
The solution to (-(sqrt(x)+6))/((sqrt(x)-2))<3 is x>4