What is expand ((x+1)^5)/(x^6+2x^4+x^2) ?

The solution to expand ((x+1)^5)/(x^6+2x^4+x^2) is (x^5+5x^4+10x^3+10x^2+5x+1)/(x^6+2x^4+x^2)

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expand ((x+1)^5)/(x^6+2x^4+x^2)

expand

\frac{( x + 1 ) ^{5}}{x ^{6} + 2 x ^{4} + x ^{2}}

\frac{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1}{x ^{6} + 2 x ^{4} + x ^{2}}

Solution steps

\frac{( x + 1 ) ^{5}}{x ^{6} + 2 x ^{4} + x ^{2}}

(x + 1)^{5} = x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1

= \frac{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1}{x ^{6} + 2 x ^{4} + x ^{2}}

\frac{33 x ^{2} + 9 x + 1}{( 3 - x ) ( 7 x ^{2} + 2 )}

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

(cot (2 x) + 1) (sin (2 x) - 1)

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

\frac{10 ( x - 4 )}{3}

What is expand ((x+1)^5)/(x^6+2x^4+x^2) ?
The solution to expand ((x+1)^5)/(x^6+2x^4+x^2) is (x^5+5x^4+10x^3+10x^2+5x+1)/(x^6+2x^4+x^2)