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\frac{\left(x^{2}-3x+2\right)\left(x^{2}-2x-3\right)}{\left(x^{2}-5x+6\right)\left(x^{2}-1\right)}\times \frac{x^{2}+4x+4}{x^{2}+3x+2}
Divide \frac{x^{2}-3x+2}{x^{2}-5x+6} by \frac{x^{2}-1}{x^{2}-2x-3} by multiplying \frac{x^{2}-3x+2}{x^{2}-5x+6} by the reciprocal of \frac{x^{2}-1}{x^{2}-2x-3}.
\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+1\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+1\right)}\times \frac{x^{2}+4x+4}{x^{2}+3x+2}
Factor the expressions that are not already factored in \frac{\left(x^{2}-3x+2\right)\left(x^{2}-2x-3\right)}{\left(x^{2}-5x+6\right)\left(x^{2}-1\right)}.
1\times \frac{x^{2}+4x+4}{x^{2}+3x+2}
Cancel out \left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+1\right) in both numerator and denominator.
1\times \frac{\left(x+2\right)^{2}}{\left(x+1\right)\left(x+2\right)}
Factor the expressions that are not already factored in \frac{x^{2}+4x+4}{x^{2}+3x+2}.
1\times \frac{x+2}{x+1}
Cancel out x+2 in both numerator and denominator.
\frac{x+2}{x+1}
Express 1\times \frac{x+2}{x+1} as a single fraction.
\frac{\left(x^{2}-3x+2\right)\left(x^{2}-2x-3\right)}{\left(x^{2}-5x+6\right)\left(x^{2}-1\right)}\times \frac{x^{2}+4x+4}{x^{2}+3x+2}
Divide \frac{x^{2}-3x+2}{x^{2}-5x+6} by \frac{x^{2}-1}{x^{2}-2x-3} by multiplying \frac{x^{2}-3x+2}{x^{2}-5x+6} by the reciprocal of \frac{x^{2}-1}{x^{2}-2x-3}.
\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+1\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+1\right)}\times \frac{x^{2}+4x+4}{x^{2}+3x+2}
Factor the expressions that are not already factored in \frac{\left(x^{2}-3x+2\right)\left(x^{2}-2x-3\right)}{\left(x^{2}-5x+6\right)\left(x^{2}-1\right)}.
1\times \frac{x^{2}+4x+4}{x^{2}+3x+2}
Cancel out \left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+1\right) in both numerator and denominator.
1\times \frac{\left(x+2\right)^{2}}{\left(x+1\right)\left(x+2\right)}
Factor the expressions that are not already factored in \frac{x^{2}+4x+4}{x^{2}+3x+2}.
1\times \frac{x+2}{x+1}
Cancel out x+2 in both numerator and denominator.
\frac{x+2}{x+1}
Express 1\times \frac{x+2}{x+1} as a single fraction.