What is expand (6(3x^2+2)+t(3x^2+2)^2)/(tx) ?

The solution to expand (6(3x^2+2)+t(3x^2+2)^2)/(tx) is (18x)/t+(12)/(xt)+9x^3+12x+4/x

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expand (6(3x^2+2)+t(3x^2+2)^2)/(tx)

expand

\frac{6 ( 3 x ^{2} + 2 ) + t ( 3 x ^{2} + 2 ) ^{2}}{t x}

\frac{18 x}{t} + \frac{12}{x t} + 9 x^{3} + 12 x + \frac{4}{x}

Solution steps

\frac{6 ( 3 x ^{2} + 2 ) + t ( 3 x ^{2} + 2 ) ^{2}}{t x}

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

= \frac{6 ( 3 x ^{2} + 2 ) + t ( 9 x ^{4} + 12 x ^{2} + 4 )}{x t}

Expand

6 (3 x^{2} + 2) + t (9 x^{4} + 12 x^{2} + 4) : 18 x^{2} + 12 + 9 x^{4} t + 12 x^{2} t + 4 t

= \frac{18 x ^{2} + 12 + 9 x ^{4} t + 12 x ^{2} t + 4 t}{x t}

Apply the fraction rule:

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

\frac{18 x ^{2} + 12 + 9 x ^{4} t + 12 x ^{2} t + 4 t}{t x} = \frac{18 x ^{2}}{t x} + \frac{12}{t x} + \frac{9 x ^{4} t}{t x} + \frac{12 x ^{2} t}{t x} + \frac{4 t}{t x}

= \frac{18 x ^{2}}{x t} + \frac{12}{x t} + \frac{9 x ^{4} t}{x t} + \frac{12 x ^{2} t}{x t} + \frac{4 t}{x t}

\frac{18 x ^{2}}{t x} = \frac{18 x}{t}

\frac{9 x ^{4} t}{t x} = 9 x^{3}

\frac{12 x ^{2} t}{t x} = 12 x

\frac{4 t}{t x} = \frac{4}{x}

= \frac{18 x}{t} + \frac{12}{x t} + 9 x^{3} + 12 x + \frac{4}{x}

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(5 t^{2} + t - t^{3}) \cdot (sin (t) - cos (t))

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

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What is expand (6(3x^2+2)+t(3x^2+2)^2)/(tx) ?
The solution to expand (6(3x^2+2)+t(3x^2+2)^2)/(tx) is (18x)/t+(12)/(xt)+9x^3+12x+4/x