What is expand ((3x+2)^2)/(x^4) ?

The solution to expand ((3x+2)^2)/(x^4) is 9/(x^2)+(12)/(x^3)+4/(x^4)

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expand ((3x+2)^2)/(x^4)

expand

\frac{( 3 x + 2 ) ^{2}}{x ^{4}}

\frac{9}{x ^{2}} + \frac{12}{x ^{3}} + \frac{4}{x ^{4}}

Solution steps

\frac{( 3 x + 2 ) ^{2}}{x ^{4}}

(3 x + 2)^{2} = 9 x^{2} + 12 x + 4

= \frac{9 x ^{2} + 12 x + 4}{x ^{4}}

Apply the fraction rule:

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

\frac{9 x ^{2} + 12 x + 4}{x ^{4}} = \frac{9 x ^{2}}{x ^{4}} + \frac{12 x}{x ^{4}} + \frac{4}{x ^{4}}

= \frac{9 x ^{2}}{x ^{4}} + \frac{12 x}{x ^{4}} + \frac{4}{x ^{4}}

Cancel

\frac{9 x ^{2}}{x ^{4}} : \frac{9}{x ^{2}}

= \frac{9}{x ^{2}} + \frac{12 x}{x ^{4}} + \frac{4}{x ^{4}}

Cancel

\frac{12 x}{x ^{4}} : \frac{12}{x ^{3}}

= \frac{9}{x ^{2}} + \frac{12}{x ^{3}} + \frac{4}{x ^{4}}

4 [k (k + 1) (k - 1)]

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

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

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

3 \frac{d}{d x} ((x - 3)^{2} x^{2})

What is expand ((3x+2)^2)/(x^4) ?
The solution to expand ((3x+2)^2)/(x^4) is 9/(x^2)+(12)/(x^3)+4/(x^4)