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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

\frac{ln ( n + 1 )}{( n + 1 ) ^{3}}

\frac{( 131 x - 25 )}{( ( x - 11 ) ( x + 13 ) )}

\frac{1}{s ( s t + 1 )}

\frac{2 a ^{2} + 36 a - 230}{( a - 8 ) ( a - 7 ) ( a + 3 )}

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

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