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

The solution to expand (x^2+5)/((x-1)(x^2+4)^2) is (x^2+5)/(x^5+8x^3+16x-x^4-8x^2-16)

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

expand

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

\frac{x ^{2} + 5}{x ^{5} + 8 x ^{3} + 16 x - x ^{4} - 8 x ^{2} - 16}

Solution steps

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

(x^{2} + 4)^{2} = x^{4} + 8 x^{2} + 16

= \frac{x ^{2} + 5}{( x - 1 ) ( x ^{4} + 8 x ^{2} + 16 )}

Expand

(x - 1) (x^{4} + 8 x^{2} + 16) : x^{5} + 8 x^{3} + 16 x - x^{4} - 8 x^{2} - 16

= \frac{x ^{2} + 5}{x ^{5} + 8 x ^{3} + 16 x - x ^{4} - 8 x ^{2} - 16}

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

\frac{5 x ^{2} - 36 x + 48}{x ( x - 4 ) ^{2}}

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

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

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

What is expand (x^2+5)/((x-1)(x^2+4)^2) ?
The solution to expand (x^2+5)/((x-1)(x^2+4)^2) is (x^2+5)/(x^5+8x^3+16x-x^4-8x^2-16)