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

The solution to expand (x(x-1)^2)/((x+3)^3) is (x^3-2x^2+x)/(x^3+9x^2+27x+27)

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

expand

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

\frac{x ^{3} - 2 x ^{2} + x}{x ^{3} + 9 x ^{2} + 27 x + 27}

Solution steps

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

(x + 3)^{3} = x^{3} + 9 x^{2} + 27 x + 27

= \frac{x ( x - 1 ) ^{2}}{x ^{3} + 9 x ^{2} + 27 x + 27}

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

= \frac{x ( x ^{2} - 2 x + 1 )}{x ^{3} + 9 x ^{2} + 27 x + 27}

Expand

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

= \frac{x ^{3} - 2 x ^{2} + x}{x ^{3} + 9 x ^{2} + 27 x + 27}

- \frac{3}{13} e^{(- 2 + 3 i) t}

(9 x^{2} + y - 1) d x - (4 y - x) d y

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

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

\frac{14}{3 ( 2 s + 3 )}

What is expand (x(x-1)^2)/((x+3)^3) ?
The solution to expand (x(x-1)^2)/((x+3)^3) is (x^3-2x^2+x)/(x^3+9x^2+27x+27)