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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

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

Simplify

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

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

50 \times 50

\frac{x + 3}{x ^{2} - 81} \cdot \frac{3 x - 27}{3 x + 9}

\frac{2}{5} \div \frac{1}{2}

(5^{2})^{5}

(12 + 5 i) - (2 - i)

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