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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

3 - \frac{7 - 2 t}{3} - t

(e^{x} + 1) (6 x^{2} - 4 x)

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

\frac{x ^{2} + 14 x + 1}{( x + 1 ) ^{2}}

(x + y = 7,) (x^{2} - y^{2} = 21)

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