What is expand ((x^6-4)^2)/(16x^6) ?

The solution to expand ((x^6-4)^2)/(16x^6) is (x^6)/(16)-1/2+1/(x^6)

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expand ((x^6-4)^2)/(16x^6)

expand

\frac{( x ^{6} - 4 ) ^{2}}{16 x ^{6}}

\frac{x ^{6}}{16} - \frac{1}{2} + \frac{1}{x ^{6}}

Solution steps

\frac{( x ^{6} - 4 ) ^{2}}{16 x ^{6}}

(x^{6} - 4)^{2} = x^{12} - 8 x^{6} + 16

= \frac{x ^{12} - 8 x ^{6} + 16}{16 x ^{6}}

Apply the fraction rule:

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

\frac{x ^{12} - 8 x ^{6} + 16}{16 x ^{6}} = \frac{x ^{12}}{16 x ^{6}} - \frac{8 x ^{6}}{16 x ^{6}} + \frac{16}{16 x ^{6}}

= \frac{x ^{12}}{16 x ^{6}} - \frac{8 x ^{6}}{16 x ^{6}} + \frac{16}{16 x ^{6}}

Cancel

\frac{x ^{12}}{16 x ^{6}} : \frac{x ^{6}}{16}

= \frac{x ^{6}}{16} - \frac{8 x ^{6}}{16 x ^{6}} + \frac{16}{16 x ^{6}}

Cancel

\frac{8 x ^{6}}{16 x ^{6}} : \frac{1}{2}

= \frac{x ^{6}}{16} - \frac{1}{2} + \frac{16}{16 x ^{6}}

Divide the numbers:

\frac{16}{16} = 1

= \frac{x ^{6}}{16} - \frac{1}{2} + \frac{1}{x ^{6}}

\frac{6 x ^{2} - 7 x - 1}{( x - 1 ) ( x + 1 ) ( x - 2 )}

(7 + 3) (7 - 3)

3 (6 + 7)

\frac{( K ( s + 0.5 ) )}{s}

(x - 6) (x - 2 + 2)

What is expand ((x^6-4)^2)/(16x^6) ?
The solution to expand ((x^6-4)^2)/(16x^6) is (x^6)/(16)-1/2+1/(x^6)