What is expand (2(6-x^2)^2)/(x^2) ?

The solution to expand (2(6-x^2)^2)/(x^2) is (72)/(x^2)-24+2x^2

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expand (2(6-x^2)^2)/(x^2)

expand

\frac{2 ( 6 - x ^{2} ) ^{2}}{x ^{2}}

\frac{72}{x ^{2}} - 24 + 2 x^{2}

Solution steps

\frac{2 ( 6 - x ^{2} ) ^{2}}{x ^{2}}

(6 - x^{2})^{2} = 36 - 12 x^{2} + x^{4}

= \frac{2 ( x ^{4} - 12 x ^{2} + 36 )}{x ^{2}}

Expand

2 (36 - 12 x^{2} + x^{4}) : 72 - 24 x^{2} + 2 x^{4}

= \frac{72 - 24 x ^{2} + 2 x ^{4}}{x ^{2}}

Apply the fraction rule:

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

\frac{72 - 24 x ^{2} + 2 x ^{4}}{x ^{2}} = \frac{72}{x ^{2}} - \frac{24 x ^{2}}{x ^{2}} + \frac{2 x ^{4}}{x ^{2}}

= \frac{72}{x ^{2}} - \frac{24 x ^{2}}{x ^{2}} + \frac{2 x ^{4}}{x ^{2}}

Cancel

\frac{24 x ^{2}}{x ^{2}} : 24

= \frac{72}{x ^{2}} - 24 + \frac{2 x ^{4}}{x ^{2}}

Cancel

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

= \frac{72}{x ^{2}} - 24 + 2 x^{2}

2 π - 2 π x (2 - 2 x^{2})

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

(\frac{1}{3 x} + (- 3) x^{2})^{8}

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

(sec (x) - 1) cot (x) - csc (x)

What is expand (2(6-x^2)^2)/(x^2) ?
The solution to expand (2(6-x^2)^2)/(x^2) is (72)/(x^2)-24+2x^2