$$\frac{7}{x-6}\cdot\frac{5}{5-x}$$
$\frac{35}{\left(5-x\right)\left(x-6\right)}$
$$\frac{7\times 5}{\left(x-6\right)\left(5-x\right)}$$
$$\frac{35}{\left(x-6\right)\left(5-x\right)}$$
$$\frac{35}{5x-x^{2}-30+6x}$$
$$\frac{35}{11x-x^{2}-30}$$
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$\frac{35\left(2x-11\right)}{\left(\left(5-x\right)\left(x-6\right)\right)^{2}}$
