What is x/(sqrt(x+1)+1) ?

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

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simplify x/(sqrt(x+1)+1)

simplify

\frac{x}{x + 1 + 1}

x + 1 - 1

Solution steps

\frac{x}{x + 1 + 1}

Multiply by the conjugate

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

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

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

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

Cancel the common factor:

x

= x + 1 - 1

5 x^{2} - 13 x y - 6 y^{2}

\frac{1}{5} \times \frac{2}{3}

8 6^{2}

\frac{5}{\frac{1}{6} + \frac{1}{x + 1}}

2.89