What is expand ((x^2+1)sqrt(x^2-4))/(x^2) ?

The solution to expand ((x^2+1)sqrt(x^2-4))/(x^2) is sqrt(x^2-4)+(sqrt(x^2-4))/(x^2)

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expand ((x^2+1)sqrt(x^2-4))/(x^2)

expand

\frac{( x ^{2} + 1 ) x ^{2} - 4}{x ^{2}}

x^{2} - 4 + \frac{x ^{2} - 4}{x ^{2}}

Solution steps

\frac{( x ^{2} + 1 ) x ^{2} - 4}{x ^{2}}

Expand

(x^{2} + 1) x^{2} - 4 : x^{2} x^{2} - 4 + x^{2} - 4

= \frac{x ^{2} x ^{2} - 4 + x ^{2} - 4}{x ^{2}}

Apply the fraction rule:

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

\frac{x ^{2} x ^{2} - 4 + x ^{2} - 4}{x ^{2}} = \frac{x ^{2} x ^{2} - 4}{x ^{2}} + \frac{x ^{2} - 4}{x ^{2}}

= \frac{x ^{2} x ^{2} - 4}{x ^{2}} + \frac{x ^{2} - 4}{x ^{2}}

Cancel

\frac{x ^{2} x ^{2} - 4}{x ^{2}} : x^{2} - 4

= x^{2} - 4 + \frac{x ^{2} - 4}{x ^{2}}

(x - \frac{2}{3})^{8}

\frac{8 x - 2}{( x - 1 ) ^{2} ( x + 2 )}

sin^{2} (2 x) \cdot (cot^{2} (x) - tan^{2} (x))

\frac{( s - 1 ) \cdot ( s + 7 )}{( s + 1 ) \cdot ( s - 2 ) \cdot ( s + 3 )}

(x^{2} + y^{2}) d x + y^{2} d y

What is expand ((x^2+1)sqrt(x^2-4))/(x^2) ?
The solution to expand ((x^2+1)sqrt(x^2-4))/(x^2) is sqrt(x^2-4)+(sqrt(x^2-4))/(x^2)