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\frac{\left(x^{2}+6x+9\right)\left(x^{2}-1\right)}{\left(x-1\right)\left(x^{2}-9\right)}
Divide \frac{x^{2}+6x+9}{x-1} by \frac{x^{2}-9}{x^{2}-1} by multiplying \frac{x^{2}+6x+9}{x-1} by the reciprocal of \frac{x^{2}-9}{x^{2}-1}.
\frac{\left(x-1\right)\left(x+1\right)\left(x+3\right)^{2}}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{\left(x+1\right)\left(x+3\right)}{x-3}
Cancel out \left(x-1\right)\left(x+3\right) in both numerator and denominator.
\frac{x^{2}+4x+3}{x-3}
Expand the expression.
\frac{\left(x^{2}+6x+9\right)\left(x^{2}-1\right)}{\left(x-1\right)\left(x^{2}-9\right)}
Divide \frac{x^{2}+6x+9}{x-1} by \frac{x^{2}-9}{x^{2}-1} by multiplying \frac{x^{2}+6x+9}{x-1} by the reciprocal of \frac{x^{2}-9}{x^{2}-1}.
\frac{\left(x-1\right)\left(x+1\right)\left(x+3\right)^{2}}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{\left(x+1\right)\left(x+3\right)}{x-3}
Cancel out \left(x-1\right)\left(x+3\right) in both numerator and denominator.
\frac{x^{2}+4x+3}{x-3}
Expand the expression.