What is expand ((2x^2+9)(x^2+2))/(x^2) ?

The solution to expand ((2x^2+9)(x^2+2))/(x^2) is 2x^2+13+(18)/(x^2)

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expand ((2x^2+9)(x^2+2))/(x^2)

expand

\frac{( 2 x ^{2} + 9 ) ( x ^{2} + 2 )}{x ^{2}}

2 x^{2} + 13 + \frac{18}{x ^{2}}

Solution steps

\frac{( 2 x ^{2} + 9 ) ( x ^{2} + 2 )}{x ^{2}}

Expand

(2 x^{2} + 9) (x^{2} + 2) : 2 x^{4} + 13 x^{2} + 18

= \frac{2 x ^{4} + 13 x ^{2} + 18}{x ^{2}}

Apply the fraction rule:

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

\frac{2 x ^{4} + 13 x ^{2} + 18}{x ^{2}} = \frac{2 x ^{4}}{x ^{2}} + \frac{13 x ^{2}}{x ^{2}} + \frac{18}{x ^{2}}

= \frac{2 x ^{4}}{x ^{2}} + \frac{13 x ^{2}}{x ^{2}} + \frac{18}{x ^{2}}

Cancel

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

= 2 x^{2} + \frac{13 x ^{2}}{x ^{2}} + \frac{18}{x ^{2}}

Cancel

\frac{13 x ^{2}}{x ^{2}} : 13

= 2 x^{2} + 13 + \frac{18}{x ^{2}}

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What is expand ((2x^2+9)(x^2+2))/(x^2) ?
The solution to expand ((2x^2+9)(x^2+2))/(x^2) is 2x^2+13+(18)/(x^2)