What is expand ((2t^2+1)^2)/(t^2) ?

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

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expand ((2t^2+1)^2)/(t^2)

expand

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

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

Solution steps

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

(2 t^{2} + 1)^{2} = 4 t^{4} + 4 t^{2} + 1

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

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

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