What is (1/(x^2))/((1+1/(x^2))^{3/2)} ?

The solution to (1/(x^2))/((1+1/(x^2))^{3/2)} is x/((x^2+1)^{3/2)}

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simplify (1/(x^2))/((1+1/(x^2))^{3/2)}

simplify

\frac{\frac{1}{x ^{2}}}{( 1 + \frac{1}{x ^{2}} ) ^{\frac{3}{2}}}

\frac{x}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{\frac{1}{x ^{2}}}{( 1 + \frac{1}{x ^{2}} ) ^{\frac{3}{2}}}

Apply the fraction rule:

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

= \frac{1}{x ^{2} ( 1 + \frac{1}{x ^{2}} ) ^{\frac{3}{2}}}

Simplify

x^{2} (1 + \frac{1}{x ^{2}})^{\frac{3}{2}} : \frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{x}

= \frac{1}{\frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{x}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

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

\frac{x - ( x - 1 ) \cdot ( x - 2 )}{( x ^{2} )}

\frac{( 5 ^{n + 2} - 5 ^{n + 1} )}{( 5 ^{n + 3} )}

(3.7 x 1 0^{- 3}) - (2.9 x 1 0^{- 5})

9 a^{2} - 4 b^{2} - 6 a + 1

What is (1/(x^2))/((1+1/(x^2))^{3/2)} ?
The solution to (1/(x^2))/((1+1/(x^2))^{3/2)} is x/((x^2+1)^{3/2)}