Final Answer
$\frac{1}{\sqrt{1+x}x}$
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Step-by-step Solution
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1
Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number
$\frac{\sqrt{1+x}+\frac{-1}{\sqrt{1+x}}}{x^2}$
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$\frac{\sqrt{1+x}+\frac{-1}{\sqrt{1+x}}}{x^2}$
Learn how to solve problems step by step online. Simplify the expression ((1+x)^1/2-(1+x)^(-1/2))/(x^2). Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Combine \sqrt{1+x}+\frac{-1}{\sqrt{1+x}} in a single fraction. Subtract the values 1 and -1. Divide fractions \frac{\frac{x}{\sqrt{1+x}}}{x^2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
Final Answer
$\frac{1}{\sqrt{1+x}x}$