What is expand-(a(-a^2+3a-1))/((a-2)(a-1)^2) ?

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

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expand-(a(-a^2+3a-1))/((a-2)(a-1)^2)

expand

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

- \frac{- a ^{3} + 3 a ^{2} - a}{a ^{3} - 4 a ^{2} + 5 a - 2}

Solution steps

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

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

= - \frac{a ( - a ^{2} + 3 a - 1 )}{( a - 2 ) ( a ^{2} - 2 a + 1 )}

Expand

(a - 2) (a^{2} - 2 a + 1) : a^{3} - 4 a^{2} + 5 a - 2

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

Expand

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

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

(t + π) e^{- in wt}

\frac{3 x ^{7}}{x ^{2}}

\frac{in t ( 4 w - 11 )}{( 2 w ^{2} + 7 w - 4 ) d w}

4 ((3 x - 2) x)

1 5^{x (x + 3)}

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