What is 1/(sqrt(x+1)+\sqrt{x)} ?

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

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simplify 1/(sqrt(x+1)+\sqrt{x)}

simplify

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

x + 1 - x

Solution steps

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

Multiply by the conjugate

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

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

1 \cdot (x + 1 - x) = x + 1 - x

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

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

Apply rule

\frac{a}{1} = a

= x + 1 - x

\frac{5}{3} \times 6

4 x^{18}

\frac{2}{3} x^{\frac{- 1}{3}}

8 a^{2} + 2 a - 1

4 i \cdot (- 3) i

What is 1/(sqrt(x+1)+\sqrt{x)} ?
The solution to 1/(sqrt(x+1)+\sqrt{x)} is sqrt(x+1)-sqrt(x)