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\frac{\left(x^{2}-49\right)\times 63}{\left(81x+567\right)\left(x-7\right)}
Divide \frac{x^{2}-49}{81x+567} by \frac{x-7}{63} by multiplying \frac{x^{2}-49}{81x+567} by the reciprocal of \frac{x-7}{63}.
\frac{63\left(x-7\right)\left(x+7\right)}{81\left(x-7\right)\left(x+7\right)}
Factor the expressions that are not already factored.
\frac{7}{9}
Cancel out 9\left(x-7\right)\left(x+7\right) in both numerator and denominator.