Evaluate
-\frac{a^{2}+9}{2a\left(a^{2}-9\right)}
Expand
-\frac{a^{2}+9}{2a\left(a^{2}-9\right)}
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\frac{5a+3}{2a\left(a+3\right)}+\frac{6-3a}{\left(a-3\right)\left(a+3\right)}
Factor 2a^{2}+6a. Factor a^{2}-9.
\frac{\left(5a+3\right)\left(a-3\right)}{2a\left(a-3\right)\left(a+3\right)}+\frac{\left(6-3a\right)\times 2a}{2a\left(a-3\right)\left(a+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a\left(a+3\right) and \left(a-3\right)\left(a+3\right) is 2a\left(a-3\right)\left(a+3\right). Multiply \frac{5a+3}{2a\left(a+3\right)} times \frac{a-3}{a-3}. Multiply \frac{6-3a}{\left(a-3\right)\left(a+3\right)} times \frac{2a}{2a}.
\frac{\left(5a+3\right)\left(a-3\right)+\left(6-3a\right)\times 2a}{2a\left(a-3\right)\left(a+3\right)}
Since \frac{\left(5a+3\right)\left(a-3\right)}{2a\left(a-3\right)\left(a+3\right)} and \frac{\left(6-3a\right)\times 2a}{2a\left(a-3\right)\left(a+3\right)} have the same denominator, add them by adding their numerators.
\frac{5a^{2}-15a+3a-9+12a-6a^{2}}{2a\left(a-3\right)\left(a+3\right)}
Do the multiplications in \left(5a+3\right)\left(a-3\right)+\left(6-3a\right)\times 2a.
\frac{-a^{2}-9}{2a\left(a-3\right)\left(a+3\right)}
Combine like terms in 5a^{2}-15a+3a-9+12a-6a^{2}.
\frac{-a^{2}-9}{2a^{3}-18a}
Expand 2a\left(a-3\right)\left(a+3\right).
\frac{5a+3}{2a\left(a+3\right)}+\frac{6-3a}{\left(a-3\right)\left(a+3\right)}
Factor 2a^{2}+6a. Factor a^{2}-9.
\frac{\left(5a+3\right)\left(a-3\right)}{2a\left(a-3\right)\left(a+3\right)}+\frac{\left(6-3a\right)\times 2a}{2a\left(a-3\right)\left(a+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a\left(a+3\right) and \left(a-3\right)\left(a+3\right) is 2a\left(a-3\right)\left(a+3\right). Multiply \frac{5a+3}{2a\left(a+3\right)} times \frac{a-3}{a-3}. Multiply \frac{6-3a}{\left(a-3\right)\left(a+3\right)} times \frac{2a}{2a}.
\frac{\left(5a+3\right)\left(a-3\right)+\left(6-3a\right)\times 2a}{2a\left(a-3\right)\left(a+3\right)}
Since \frac{\left(5a+3\right)\left(a-3\right)}{2a\left(a-3\right)\left(a+3\right)} and \frac{\left(6-3a\right)\times 2a}{2a\left(a-3\right)\left(a+3\right)} have the same denominator, add them by adding their numerators.
\frac{5a^{2}-15a+3a-9+12a-6a^{2}}{2a\left(a-3\right)\left(a+3\right)}
Do the multiplications in \left(5a+3\right)\left(a-3\right)+\left(6-3a\right)\times 2a.
\frac{-a^{2}-9}{2a\left(a-3\right)\left(a+3\right)}
Combine like terms in 5a^{2}-15a+3a-9+12a-6a^{2}.
\frac{-a^{2}-9}{2a^{3}-18a}
Expand 2a\left(a-3\right)\left(a+3\right).
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