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\frac{q-8}{2q+3}
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\frac{q-8}{2q+3}
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\frac{\left(q^{2}-14q+48\right)\left(q^{2}-6q-16\right)}{\left(2q^{2}-13q-24\right)\left(q^{2}-4q-12\right)}
Divide \frac{q^{2}-14q+48}{2q^{2}-13q-24} by \frac{q^{2}-4q-12}{q^{2}-6q-16} by multiplying \frac{q^{2}-14q+48}{2q^{2}-13q-24} by the reciprocal of \frac{q^{2}-4q-12}{q^{2}-6q-16}.
\frac{\left(q-6\right)\left(q+2\right)\left(q-8\right)^{2}}{\left(q-8\right)\left(q-6\right)\left(q+2\right)\left(2q+3\right)}
Factor the expressions that are not already factored.
\frac{q-8}{2q+3}
Cancel out \left(q-8\right)\left(q-6\right)\left(q+2\right) in both numerator and denominator.
\frac{\left(q^{2}-14q+48\right)\left(q^{2}-6q-16\right)}{\left(2q^{2}-13q-24\right)\left(q^{2}-4q-12\right)}
Divide \frac{q^{2}-14q+48}{2q^{2}-13q-24} by \frac{q^{2}-4q-12}{q^{2}-6q-16} by multiplying \frac{q^{2}-14q+48}{2q^{2}-13q-24} by the reciprocal of \frac{q^{2}-4q-12}{q^{2}-6q-16}.
\frac{\left(q-6\right)\left(q+2\right)\left(q-8\right)^{2}}{\left(q-8\right)\left(q-6\right)\left(q+2\right)\left(2q+3\right)}
Factor the expressions that are not already factored.
\frac{q-8}{2q+3}
Cancel out \left(q-8\right)\left(q-6\right)\left(q+2\right) in both numerator and denominator.
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