What is expand ((x^6-1)^2)/(4x^6) ?

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

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expand ((x^6-1)^2)/(4x^6)

expand

\frac{( x ^{6} - 1 ) ^{2}}{4 x ^{6}}

\frac{x ^{6}}{4} - \frac{1}{2} + \frac{1}{4 x ^{6}}

Solution steps

\frac{( x ^{6} - 1 ) ^{2}}{4 x ^{6}}

(x^{6} - 1)^{2} = x^{12} - 2 x^{6} + 1

= \frac{x ^{12} - 2 x ^{6} + 1}{4 x ^{6}}

Apply the fraction rule:

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

\frac{x ^{12} - 2 x ^{6} + 1}{4 x ^{6}} = \frac{x ^{12}}{4 x ^{6}} - \frac{2 x ^{6}}{4 x ^{6}} + \frac{1}{4 x ^{6}}

= \frac{x ^{12}}{4 x ^{6}} - \frac{2 x ^{6}}{4 x ^{6}} + \frac{1}{4 x ^{6}}

Cancel

\frac{x ^{12}}{4 x ^{6}} : \frac{x ^{6}}{4}

= \frac{x ^{6}}{4} - \frac{2 x ^{6}}{4 x ^{6}} + \frac{1}{4 x ^{6}}

Cancel

\frac{2 x ^{6}}{4 x ^{6}} : \frac{1}{2}

= \frac{x ^{6}}{4} - \frac{1}{2} + \frac{1}{4 x ^{6}}

\frac{2 ( 15 + 15 )}{21}

\frac{x ^{3} + x ^{2}}{( x ^{2} + 4 ) ^{2}}

e^{- 3 (- x + t)} - e^{3 x}

5 sin (5 x) (1 - e^{4 x})

(x + 10) (x - 10)

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