What is the answer to sqrt(x+2)-2/(sqrt(x+2))=1 ?

The answer to sqrt(x+2)-2/(sqrt(x+2))=1 is x=2

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sqrt(x+2)-2/(sqrt(x+2))=1

x + 2 - \frac{2}{x + 2} = 1

x = 2

Solution steps

x + 2 - \frac{2}{x + 2} = 1

Multiply both sides by

x + 2

x + 2 x + 2 - \frac{2}{x + 2} x + 2 = 1 \cdot x + 2

Simplify

(x + 2)^{2} - 2 = x + 2

Move

x + 2

to the left side

(x + 2)^{2} - 2 - x + 2 = 0

Factor

(x + 2)^{2} - 2 - x + 2 : (x + 2 + 1) (x + 2 - 2)

(x + 2 + 1) (x + 2 - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 + 1 = 0 or x + 2 - 2 = 0

Solve

x + 2 + 1 = 0 :

No Solution for

x \in R

Solve

x + 2 - 2 = 0 : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

x - 2 = x + 1

x - 2 = x + 2

x - 2 + x - 2 = 2

2 x - 5 = 4 x - 7

What is the answer to sqrt(x+2)-2/(sqrt(x+2))=1 ?
The answer to sqrt(x+2)-2/(sqrt(x+2))=1 is x=2
Solve for x: sqrt(x+2)-2/(sqrt(x+2))=1
The solution is x=2