What is expand 1/(s^2-s+2)*(12(2s-1))/(s+1) ?

The solution to expand 1/(s^2-s+2)*(12(2s-1))/(s+1) is (24s-12)/(s^3+s+2)

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expand 1/(s^2-s+2)*(12(2s-1))/(s+1)

expand

\frac{1}{s ^{2} - s + 2} \cdot \frac{12 ( 2 s - 1 )}{s + 1}

\frac{24 s - 12}{s ^{3} + s + 2}

Solution steps

\frac{1}{s ^{2} - s + 2} \cdot \frac{12 ( 2 s - 1 )}{s + 1}

\frac{12 ( 2 s - 1 )}{s + 1} = \frac{24 s - 12}{s + 1}

= \frac{1}{s ^{2} - s + 2} \cdot \frac{24 s - 12}{s + 1}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot ( 24 s - 12 )}{( s ^{2} - s + 2 ) ( s + 1 )}

1 \cdot (24 s - 12) = 24 s - 12

= \frac{24 s - 12}{( s ^{2} - s + 2 ) ( s + 1 )}

Expand

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

= \frac{24 s - 12}{s ^{3} + s + 2}

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What is expand 1/(s^2-s+2)*(12(2s-1))/(s+1) ?
The solution to expand 1/(s^2-s+2)*(12(2s-1))/(s+1) is (24s-12)/(s^3+s+2)