What is expand ((x+1)^2(x-3))/((x-4)^3(x+5)) ?

The solution to expand ((x+1)^2(x-3))/((x-4)^3(x+5)) is (x^3-x^2-5x-3)/(x^4-7x^3-12x^2+176x-320)

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expand ((x+1)^2(x-3))/((x-4)^3(x+5))

expand

\frac{( x + 1 ) ^{2} ( x - 3 )}{( x - 4 ) ^{3} ( x + 5 )}

\frac{x ^{3} - x ^{2} - 5 x - 3}{x ^{4} - 7 x ^{3} - 12 x ^{2} + 176 x - 320}

Solution steps

\frac{( x + 1 ) ^{2} ( x - 3 )}{( x - 4 ) ^{3} ( x + 5 )}

(x - 4)^{3} = x^{3} - 12 x^{2} + 48 x - 64

= \frac{( x + 1 ) ^{2} ( x - 3 )}{( x ^{3} - 12 x ^{2} + 48 x - 64 ) ( x + 5 )}

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

= \frac{( x ^{2} + 2 x + 1 ) ( x - 3 )}{( x ^{3} - 12 x ^{2} + 48 x - 64 ) ( x + 5 )}

Expand

(x^{3} - 12 x^{2} + 48 x - 64) (x + 5) : x^{4} - 7 x^{3} - 12 x^{2} + 176 x - 320

= \frac{( x ^{2} + 2 x + 1 ) ( x - 3 )}{x ^{4} - 7 x ^{3} - 12 x ^{2} + 176 x - 320}

Expand

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

= \frac{x ^{3} - x ^{2} - 5 x - 3}{x ^{4} - 7 x ^{3} - 12 x ^{2} + 176 x - 320}

(x + 2 - 2) \cdot (x + 2 + 2)

\frac{- 2 x ^{2} + 10 x + 4}{( x - 1 ) ( x ^{2} + 2 x + 9 )}

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

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

\frac{( 45 a ^{2} - b )}{( 30 ab )}

What is expand ((x+1)^2(x-3))/((x-4)^3(x+5)) ?
The solution to expand ((x+1)^2(x-3))/((x-4)^3(x+5)) is (x^3-x^2-5x-3)/(x^4-7x^3-12x^2+176x-320)