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\frac{\left(4a^{2}-1\right)\left(a^{2}-8-2a\right)}{\left(6a-8-a^{2}\right)\left(2a^{2}+5a+2\right)}
Divide \frac{4a^{2}-1}{6a-8-a^{2}} by \frac{2a^{2}+5a+2}{a^{2}-8-2a} by multiplying \frac{4a^{2}-1}{6a-8-a^{2}} by the reciprocal of \frac{2a^{2}+5a+2}{a^{2}-8-2a}.
\frac{\left(a-4\right)\left(2a-1\right)\left(a+2\right)\left(2a+1\right)}{\left(a-4\right)\left(a+2\right)\left(-a+2\right)\left(2a+1\right)}
Factor the expressions that are not already factored.
\frac{2a-1}{-a+2}
Cancel out \left(a-4\right)\left(a+2\right)\left(2a+1\right) in both numerator and denominator.
\frac{\left(4a^{2}-1\right)\left(a^{2}-8-2a\right)}{\left(6a-8-a^{2}\right)\left(2a^{2}+5a+2\right)}
Divide \frac{4a^{2}-1}{6a-8-a^{2}} by \frac{2a^{2}+5a+2}{a^{2}-8-2a} by multiplying \frac{4a^{2}-1}{6a-8-a^{2}} by the reciprocal of \frac{2a^{2}+5a+2}{a^{2}-8-2a}.
\frac{\left(a-4\right)\left(2a-1\right)\left(a+2\right)\left(2a+1\right)}{\left(a-4\right)\left(a+2\right)\left(-a+2\right)\left(2a+1\right)}
Factor the expressions that are not already factored.
\frac{2a-1}{-a+2}
Cancel out \left(a-4\right)\left(a+2\right)\left(2a+1\right) in both numerator and denominator.