Solve a-3/a^2-1div3a+3/a^2+2a+1+1/a-1

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Polynomial

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

Divide \frac{a-3}{a^{2}-1} by \frac{3a+3}{a^{2}+2a+1} by multiplying \frac{a-3}{a^{2}-1} by the reciprocal of \frac{3a+3}{a^{2}+2a+1}.

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

Factor the expressions that are not already factored in \frac{\left(a-3\right)\left(a^{2}+2a+1\right)}{\left(a^{2}-1\right)\left(3a+3\right)}.

\frac{a-3}{3\left(a-1\right)}+\frac{1}{a-1}

Cancel out \left(a+1\right)^{2} in both numerator and denominator.

\frac{a-3}{3\left(a-1\right)}+\frac{3}{3\left(a-1\right)}

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(a-1\right) and a-1 is 3\left(a-1\right). Multiply \frac{1}{a-1} times \frac{3}{3}.

\frac{a-3+3}{3\left(a-1\right)}

Since \frac{a-3}{3\left(a-1\right)} and \frac{3}{3\left(a-1\right)} have the same denominator, add them by adding their numerators.

\frac{a}{3\left(a-1\right)}

Combine like terms in a-3+3.

\frac{a}{3a-3}

Expand 3\left(a-1\right).