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

The solution to a/((a-1)*(a-1)^2+1) is 1/(a^2-3a+3)

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simplify a/((a-1)*(a-1)^2+1)

simplify

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

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

Solution steps

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

Simplify

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

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

Factor

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

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

Cancel the common factor:

a

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

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\frac{6 y ^{5} + 4 y ^{3} - 10 y ^{2} + 2 y}{2 y}

sin^{2} (q) + cos^{2} (q)

\frac{( 2 - x )}{( x - 2 )}

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

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