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\frac{1}{z^{2}-81}
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\frac{1}{z^{2}-81}
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\frac{z-5}{\left(z-9\right)\left(z+9\right)}-\frac{6-z}{\left(z-9\right)\left(-z-9\right)}
Factor z^{2}-81. Factor 81-z^{2}.
\frac{z-5}{\left(z-9\right)\left(z+9\right)}-\frac{-\left(6-z\right)}{\left(z-9\right)\left(z+9\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(z-9\right)\left(z+9\right) and \left(z-9\right)\left(-z-9\right) is \left(z-9\right)\left(z+9\right). Multiply \frac{6-z}{\left(z-9\right)\left(-z-9\right)} times \frac{-1}{-1}.
\frac{z-5-\left(-\left(6-z\right)\right)}{\left(z-9\right)\left(z+9\right)}
Since \frac{z-5}{\left(z-9\right)\left(z+9\right)} and \frac{-\left(6-z\right)}{\left(z-9\right)\left(z+9\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{z-5+6-z}{\left(z-9\right)\left(z+9\right)}
Do the multiplications in z-5-\left(-\left(6-z\right)\right).
\frac{1}{\left(z-9\right)\left(z+9\right)}
Combine like terms in z-5+6-z.
\frac{1}{z^{2}-81}
Expand \left(z-9\right)\left(z+9\right).
\frac{z-5}{\left(z-9\right)\left(z+9\right)}-\frac{6-z}{\left(z-9\right)\left(-z-9\right)}
Factor z^{2}-81. Factor 81-z^{2}.
\frac{z-5}{\left(z-9\right)\left(z+9\right)}-\frac{-\left(6-z\right)}{\left(z-9\right)\left(z+9\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(z-9\right)\left(z+9\right) and \left(z-9\right)\left(-z-9\right) is \left(z-9\right)\left(z+9\right). Multiply \frac{6-z}{\left(z-9\right)\left(-z-9\right)} times \frac{-1}{-1}.
\frac{z-5-\left(-\left(6-z\right)\right)}{\left(z-9\right)\left(z+9\right)}
Since \frac{z-5}{\left(z-9\right)\left(z+9\right)} and \frac{-\left(6-z\right)}{\left(z-9\right)\left(z+9\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{z-5+6-z}{\left(z-9\right)\left(z+9\right)}
Do the multiplications in z-5-\left(-\left(6-z\right)\right).
\frac{1}{\left(z-9\right)\left(z+9\right)}
Combine like terms in z-5+6-z.
\frac{1}{z^{2}-81}
Expand \left(z-9\right)\left(z+9\right).
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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