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

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

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

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

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

= 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}}

= 1 + \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}

= 1 + \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}

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

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

\frac{[ ( x + h ) + 5 ] ^{\frac{2}{3}} - ( x + 5 ) ^{\frac{2}{3}}}{h}

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