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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

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

x (4 - 5 x) \leq 0

\frac{1}{x - 2} + \frac{3}{4 x - 36} \geq 0

p^{2} - 2 p - 15

7 x^{2} - 42 x = 0

7 x^{2} = - x

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