What is expand (4x^2+16x)/((x-2)^2(x^2+4)) ?

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

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expand (4x^2+16x)/((x-2)^2(x^2+4))

expand

\frac{4 x ^{2} + 16 x}{( x - 2 ) ^{2} ( x ^{2} + 4 )}

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

Solution steps

\frac{4 x ^{2} + 16 x}{( x - 2 ) ^{2} ( x ^{2} + 4 )}

(x - 2)^{2} = x^{2} - 4 x + 4

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

Expand

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

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

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

80 (10 + 1)

2 (- 5 + 5)

- \frac{9}{2} - 8

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

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