What is expand ((s-1)s)/(s(s-1)^2-1) ?

The solution to expand ((s-1)s)/(s(s-1)^2-1) is (s^2-s)/(s^3-2s^2+s-1)

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expand ((s-1)s)/(s(s-1)^2-1)

expand

\frac{( s - 1 ) s}{s ( s - 1 ) ^{2} - 1}

\frac{s ^{2} - s}{s ^{3} - 2 s ^{2} + s - 1}

Solution steps

\frac{( s - 1 ) s}{s ( s - 1 ) ^{2} - 1}

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

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

Expand

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

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

Expand

(s - 1) s : s^{2} - s

= \frac{s ^{2} - s}{s ^{3} - 2 s ^{2} + s - 1}

\frac{3 ( k + 10 )}{( 2 x + 1 ) ( x - 3 )}

e^{4 y - x^{2} - y^{2}} (- 2 y + 4)

\frac{z ( x - y )}{x + y}

+ \frac{x ( - x + 3 ) ^{2}}{6}

(1.01)^{3}

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