What is expand ((60x+x^4+12)(x^4+4))/(48x^3) ?

The solution to expand ((60x+x^4+12)(x^4+4))/(48x^3) is (5x^2)/4+5/(x^2)+(x^5)/(48)+x/3+1/(x^3)

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expand ((60x+x^4+12)(x^4+4))/(48x^3)

expand

\frac{( 60 x + x ^{4} + 12 ) ( x ^{4} + 4 )}{48 x ^{3}}

\frac{5 x ^{2}}{4} + \frac{5}{x ^{2}} + \frac{x ^{5}}{48} + \frac{x}{3} + \frac{1}{x ^{3}}

Solution steps

\frac{( 60 x + x ^{4} + 12 ) ( x ^{4} + 4 )}{48 x ^{3}}

Expand

(60 x + x^{4} + 12) (x^{4} + 4) : 60 x^{5} + 240 x + x^{8} + 16 x^{4} + 48

= \frac{60 x ^{5} + 240 x + x ^{8} + 16 x ^{4} + 48}{48 x ^{3}}

Apply the fraction rule:

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

\frac{60 x ^{5} + 240 x + x ^{8} + 16 x ^{4} + 48}{48 x ^{3}} = \frac{60 x ^{5}}{48 x ^{3}} + \frac{240 x}{48 x ^{3}} + \frac{x ^{8}}{48 x ^{3}} + \frac{16 x ^{4}}{48 x ^{3}} + \frac{48}{48 x ^{3}}

= \frac{60 x ^{5}}{48 x ^{3}} + \frac{240 x}{48 x ^{3}} + \frac{x ^{8}}{48 x ^{3}} + \frac{16 x ^{4}}{48 x ^{3}} + \frac{48}{48 x ^{3}}

\frac{60 x ^{5}}{48 x ^{3}} = \frac{5 x ^{2}}{4}

\frac{240 x}{48 x ^{3}} = \frac{5}{x ^{2}}

\frac{x ^{8}}{48 x ^{3}} = \frac{x ^{5}}{48}

\frac{16 x ^{4}}{48 x ^{3}} = \frac{x}{3}

\frac{48}{48 x ^{3}} = \frac{1}{x ^{3}}

= \frac{5 x ^{2}}{4} + \frac{5}{x ^{2}} + \frac{x ^{5}}{48} + \frac{x}{3} + \frac{1}{x ^{3}}

\frac{\partial}{\partial t} ((y^{2}) (y - t^{2} + 1))

1 - x ((2 - x) (1 - x))

\frac{1}{s \cdot ( s - 1 )}

E [x_{(t + l)} - a x_{t} - b]^{2}

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

What is expand ((60x+x^4+12)(x^4+4))/(48x^3) ?
The solution to expand ((60x+x^4+12)(x^4+4))/(48x^3) is (5x^2)/4+5/(x^2)+(x^5)/(48)+x/3+1/(x^3)