Evaluate
\frac{a+10}{7a-40}
Expand
\frac{a+10}{7a-40}
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\frac{a\left(a^{2}-100\right)}{\left(a-10\right)\left(a^{2}+6a^{2}-40a\right)}
Divide \frac{a}{a-10} by \frac{a^{2}+6a^{2}-40a}{a^{2}-100} by multiplying \frac{a}{a-10} by the reciprocal of \frac{a^{2}+6a^{2}-40a}{a^{2}-100}.
\frac{a\left(a^{2}-100\right)}{\left(a-10\right)\left(7a^{2}-40a\right)}
Combine a^{2} and 6a^{2} to get 7a^{2}.
\frac{a\left(a-10\right)\left(a+10\right)}{a\left(a-10\right)\left(7a-40\right)}
Factor the expressions that are not already factored.
\frac{a+10}{7a-40}
Cancel out a\left(a-10\right) in both numerator and denominator.
\frac{a\left(a^{2}-100\right)}{\left(a-10\right)\left(a^{2}+6a^{2}-40a\right)}
Divide \frac{a}{a-10} by \frac{a^{2}+6a^{2}-40a}{a^{2}-100} by multiplying \frac{a}{a-10} by the reciprocal of \frac{a^{2}+6a^{2}-40a}{a^{2}-100}.
\frac{a\left(a^{2}-100\right)}{\left(a-10\right)\left(7a^{2}-40a\right)}
Combine a^{2} and 6a^{2} to get 7a^{2}.
\frac{a\left(a-10\right)\left(a+10\right)}{a\left(a-10\right)\left(7a-40\right)}
Factor the expressions that are not already factored.
\frac{a+10}{7a-40}
Cancel out a\left(a-10\right) in both numerator and denominator.
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