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

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

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

simplify

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

\frac{x + h - x}{h}

Solution steps

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

Multiply by the conjugate

\frac{x + h - x}{x + h - x}

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

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

(x + h + x) (x + h - x) = h

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

2 - 2 i

- 24 + 9

- 25 - 5

(0.7)^{4}

t^{5} + 4 t^{3}

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