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

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

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

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

x \geq - 1

Solution steps

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

Multiply both sides by

x + 1 + 1

\frac{x}{x + 1 + 1} (x + 1 + 1) = x + 1 (x + 1 + 1) - 1 \cdot (x + 1 + 1)

Simplify

x = x + 1 (x + 1 + 1) - (x + 1 + 1)

Expand

x + 1 (x + 1 + 1) - (x + 1 + 1) : x

x = x

Both sides are equal

True for all x

Verify Solutions:

x = - 1

True

, x > - 1

True

The solution is

x \geq - 1

3 - 8 x^{2} = 2 x

2 x - 2 x + 3 = 6

x - 10 = x - 1

6 \frac{x}{8} = 18

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