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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

(a^{\frac{1}{2}} - b^{\frac{1}{2}}) (a^{\frac{1}{2}} + b^{\frac{1}{2}})

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

(e^{t} - 2)^{2}

(5 - x) (5 + x)

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

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