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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

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

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

Cancel

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

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

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