Evaluate
\frac{11a+48}{\left(a+4\right)\left(a+8\right)}
Expand
\frac{11a+48}{\left(a+4\right)\left(a+8\right)}
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\frac{\left(a+5\right)\left(a+8\right)}{\left(a+4\right)\left(a+8\right)}-\frac{\left(a-2\right)\left(a+4\right)}{\left(a+4\right)\left(a+8\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+4 and a+8 is \left(a+4\right)\left(a+8\right). Multiply \frac{a+5}{a+4} times \frac{a+8}{a+8}. Multiply \frac{a-2}{a+8} times \frac{a+4}{a+4}.
\frac{\left(a+5\right)\left(a+8\right)-\left(a-2\right)\left(a+4\right)}{\left(a+4\right)\left(a+8\right)}
Since \frac{\left(a+5\right)\left(a+8\right)}{\left(a+4\right)\left(a+8\right)} and \frac{\left(a-2\right)\left(a+4\right)}{\left(a+4\right)\left(a+8\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a^{2}+8a+5a+40-a^{2}-4a+2a+8}{\left(a+4\right)\left(a+8\right)}
Do the multiplications in \left(a+5\right)\left(a+8\right)-\left(a-2\right)\left(a+4\right).
\frac{11a+48}{\left(a+4\right)\left(a+8\right)}
Combine like terms in a^{2}+8a+5a+40-a^{2}-4a+2a+8.
\frac{11a+48}{a^{2}+12a+32}
Expand \left(a+4\right)\left(a+8\right).
\frac{\left(a+5\right)\left(a+8\right)}{\left(a+4\right)\left(a+8\right)}-\frac{\left(a-2\right)\left(a+4\right)}{\left(a+4\right)\left(a+8\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+4 and a+8 is \left(a+4\right)\left(a+8\right). Multiply \frac{a+5}{a+4} times \frac{a+8}{a+8}. Multiply \frac{a-2}{a+8} times \frac{a+4}{a+4}.
\frac{\left(a+5\right)\left(a+8\right)-\left(a-2\right)\left(a+4\right)}{\left(a+4\right)\left(a+8\right)}
Since \frac{\left(a+5\right)\left(a+8\right)}{\left(a+4\right)\left(a+8\right)} and \frac{\left(a-2\right)\left(a+4\right)}{\left(a+4\right)\left(a+8\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a^{2}+8a+5a+40-a^{2}-4a+2a+8}{\left(a+4\right)\left(a+8\right)}
Do the multiplications in \left(a+5\right)\left(a+8\right)-\left(a-2\right)\left(a+4\right).
\frac{11a+48}{\left(a+4\right)\left(a+8\right)}
Combine like terms in a^{2}+8a+5a+40-a^{2}-4a+2a+8.
\frac{11a+48}{a^{2}+12a+32}
Expand \left(a+4\right)\left(a+8\right).
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Simultaneous equation
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Integration
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Limits
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