What is expand (x^3+7x+12s)/((x+1)^3(x+2)) ?

The solution to expand (x^3+7x+12s)/((x+1)^3(x+2)) is (x^3+7x+12s)/(x^4+5x^3+9x^2+7x+2)

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expand (x^3+7x+12s)/((x+1)^3(x+2))

expand

\frac{x ^{3} + 7 x + 12 s}{( x + 1 ) ^{3} ( x + 2 )}

\frac{x ^{3} + 7 x + 12 s}{x ^{4} + 5 x ^{3} + 9 x ^{2} + 7 x + 2}

Solution steps

\frac{x ^{3} + 7 x + 12 s}{( x + 1 ) ^{3} ( x + 2 )}

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

= \frac{x ^{3} + 7 x + 12 s}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x + 2 )}

Expand

(x^{3} + 3 x^{2} + 3 x + 1) (x + 2) : x^{4} + 5 x^{3} + 9 x^{2} + 7 x + 2

= \frac{x ^{3} + 7 x + 12 s}{x ^{4} + 5 x ^{3} + 9 x ^{2} + 7 x + 2}

\frac{( ( 12 + 3 x ) ^{2} )}{( 2 + x ) ^{6}}

\frac{10 s ^{3} + 20 s + 2}{( s ^{2} + 1 ) ( s ^{2} + 2 )}

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

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

\frac{s}{( s ^{2} + 2 s + 10 )}

What is expand (x^3+7x+12s)/((x+1)^3(x+2)) ?
The solution to expand (x^3+7x+12s)/((x+1)^3(x+2)) is (x^3+7x+12s)/(x^4+5x^3+9x^2+7x+2)