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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

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

\frac{( x + h ) ^{3} - 3 a x ^{2} + 2 b x + c}{h}

\frac{3 x ^{2} + 5}{2 ( x - 1 ) ^{2}}

\frac{1}{2 ( cosh ( x ) + cos ( x ) )}

(3 - 11 - x) (6 - x + 2)

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