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

The solution to expand (x+4)/((x-1)^2(x^2+1)) is (x+4)/(x^4+2x^2-2x^3-2x+1)

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expand (x+4)/((x-1)^2(x^2+1))

expand

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

\frac{x + 4}{x ^{4} + 2 x ^{2} - 2 x ^{3} - 2 x + 1}

Solution steps

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

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

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

Expand

(x^{2} - 2 x + 1) (x^{2} + 1) : x^{4} + 2 x^{2} - 2 x^{3} - 2 x + 1

= \frac{x + 4}{x ^{4} + 2 x ^{2} - 2 x ^{3} - 2 x + 1}

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

4 x^{2} (2 x + 3 x^{3} + 7 x^{2})^{3}

\frac{x ( x - 5 )}{x ^{2} - 9}

\frac{8 x + 3}{( x + 2 ) ( x + 3 )}

(- 1, 1) y (5, - \frac{7}{2})

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