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

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

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

expand

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

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

Solution steps

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

(x^{4} - 1)^{2} = x^{8} - 2 x^{4} + 1

= \frac{x ^{8} - 2 x ^{4} + 1}{4 x ^{4}}

Apply the fraction rule:

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

\frac{x ^{8} - 2 x ^{4} + 1}{4 x ^{4}} = \frac{x ^{8}}{4 x ^{4}} - \frac{2 x ^{4}}{4 x ^{4}} + \frac{1}{4 x ^{4}}

= \frac{x ^{8}}{4 x ^{4}} - \frac{2 x ^{4}}{4 x ^{4}} + \frac{1}{4 x ^{4}}

Cancel

\frac{x ^{8}}{4 x ^{4}} : \frac{x ^{4}}{4}

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

Cancel

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

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

(4 x^{3} y^{2} - 6 x^{2} y - 2 x - 3) d x + (2 x^{4} y - 2 x^{3}) d y

(k + 1)! (k + 2)

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

16 π (0.02 \cdot \frac{0.0 1 ^{2}}{2} - \frac{0.0 1 ^{3}}{3})

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

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