Simplify the following fractions \[ \left\{\frac{\frac{a-c}{1+a c}+c}{1-\frac{c(a-c)}{1+a c}}-\f...

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Simplify the following fractions
\[
\left\{\frac{\frac{a-c}{1+a c}+c}{1-\frac{c(a-c)}{1+a c}}-\frac{a-\frac{a-c}{1-a c}}{1-\frac{a(a-c)}{1-a c}}\right\} \div\left(\frac{a}{c}-\frac{c}{a}\right) .
\]
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