What is the answer to 6/(sqrt(x+8))=sqrt(x+8)-sqrt(x) ?

The answer to 6/(sqrt(x+8))=sqrt(x+8)-sqrt(x) is x=1

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6/(sqrt(x+8))=sqrt(x+8)-sqrt(x)

\frac{6}{x + 8} = x + 8 - x

x = 1

Solution steps

\frac{6}{x + 8} = x + 8 - x

Multiply both sides by

x + 8

\frac{6}{x + 8} x + 8 = x + 8 x + 8 - x x + 8

Simplify

6 = (x + 8)^{2} - x + 8 x

Expand

(x + 8)^{2} - x + 8 x : x + 8 - x + 8 x

6 = x + 8 - x + 8 x

Remove square roots

x^{2} + 4 x + 4 = x^{2} + 8 x

Solve

x^{2} + 4 x + 4 = x^{2} + 8 x : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

21 - 3 x = x - 1

4 = 3 x + 54 - 9 x + 7 x^{2}

x - 23 = 5

8 x + 25 - 2 x + 4 = 3

c, a = \frac{b - c}{2 c} + d

What is the answer to 6/(sqrt(x+8))=sqrt(x+8)-sqrt(x) ?
The answer to 6/(sqrt(x+8))=sqrt(x+8)-sqrt(x) is x=1
Solve for x: 6/(sqrt(x+8))=sqrt(x+8)-sqrt(x)
The solution is x=1