What is expand (3(x+1)^2)/(x^4) ?

The solution to expand (3(x+1)^2)/(x^4) is 3/(x^2)+6/(x^3)+3/(x^4)

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expand (3(x+1)^2)/(x^4)

expand

\frac{3 ( x + 1 ) ^{2}}{x ^{4}}

\frac{3}{x ^{2}} + \frac{6}{x ^{3}} + \frac{3}{x ^{4}}

Solution steps

\frac{3 ( x + 1 ) ^{2}}{x ^{4}}

(x + 1)^{2} = x^{2} + 2 x + 1

= \frac{3 ( x ^{2} + 2 x + 1 )}{x ^{4}}

Expand

3 (x^{2} + 2 x + 1) : 3 x^{2} + 6 x + 3

= \frac{3 x ^{2} + 6 x + 3}{x ^{4}}

Apply the fraction rule:

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

\frac{3 x ^{2} + 6 x + 3}{x ^{4}} = \frac{3 x ^{2}}{x ^{4}} + \frac{6 x}{x ^{4}} + \frac{3}{x ^{4}}

= \frac{3 x ^{2}}{x ^{4}} + \frac{6 x}{x ^{4}} + \frac{3}{x ^{4}}

Cancel

\frac{3 x ^{2}}{x ^{4}} : \frac{3}{x ^{2}}

= \frac{3}{x ^{2}} + \frac{6 x}{x ^{4}} + \frac{3}{x ^{4}}

Cancel

\frac{6 x}{x ^{4}} : \frac{6}{x ^{3}}

= \frac{3}{x ^{2}} + \frac{6}{x ^{3}} + \frac{3}{x ^{4}}

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

\frac{2 ( 3 3 - 2 )}{3}

e^{2 (a + bi)}

\frac{5 - 2 ( a + 3 b )}{2}

(3 e^{5 t} - 3 e^{4 t}) (15 e^{5 t} - 12 e^{4 t})

What is expand (3(x+1)^2)/(x^4) ?
The solution to expand (3(x+1)^2)/(x^4) is 3/(x^2)+6/(x^3)+3/(x^4)