What is expand (3x)/((x-2)(x^2+5)^3) ?

The solution to expand (3x)/((x-2)(x^2+5)^3) is (3x)/(x^7+15x^5+75x^3+125x-2x^6-30x^4-150x^2-250)

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expand (3x)/((x-2)(x^2+5)^3)

expand

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

\frac{3 x}{x ^{7} + 15 x ^{5} + 75 x ^{3} + 125 x - 2 x ^{6} - 30 x ^{4} - 150 x ^{2} - 250}

Solution steps

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

(x^{2} + 5)^{3} = x^{6} + 15 x^{4} + 75 x^{2} + 125

= \frac{3 x}{( x - 2 ) ( x ^{6} + 15 x ^{4} + 75 x ^{2} + 125 )}

Expand

(x - 2) (x^{6} + 15 x^{4} + 75 x^{2} + 125) : x^{7} + 15 x^{5} + 75 x^{3} + 125 x - 2 x^{6} - 30 x^{4} - 150 x^{2} - 250

= \frac{3 x}{x ^{7} + 15 x ^{5} + 75 x ^{3} + 125 x - 2 x ^{6} - 30 x ^{4} - 150 x ^{2} - 250}

cos (x) (csc (x) - sec (x))

(\frac{x}{2} + \frac{1}{x})^{12}

\frac{x ^{9} + 5 x ^{5} - x ^{3} + 2021}{x ^{3} ( x ^{4} - 16 )}

2 (x + Δ x)^{2}

(- 2 + \frac{3 i}{n})^{2}

What is expand (3x)/((x-2)(x^2+5)^3) ?
The solution to expand (3x)/((x-2)(x^2+5)^3) is (3x)/(x^7+15x^5+75x^3+125x-2x^6-30x^4-150x^2-250)