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-\frac{2}{a^{2}-1}
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-\frac{2}{a^{2}-1}
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a^{2}+1-\frac{a^{4}+1}{\left(a-1\right)\left(a+1\right)}
Factor a^{2}-1.
\frac{\left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{a^{4}+1}{\left(a-1\right)\left(a+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2}+1 times \frac{\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}.
\frac{\left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)-\left(a^{4}+1\right)}{\left(a-1\right)\left(a+1\right)}
Since \frac{\left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} and \frac{a^{4}+1}{\left(a-1\right)\left(a+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a^{4}-a^{2}+a^{2}-1-a^{4}-1}{\left(a-1\right)\left(a+1\right)}
Do the multiplications in \left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)-\left(a^{4}+1\right).
\frac{-2}{\left(a-1\right)\left(a+1\right)}
Combine like terms in a^{4}-a^{2}+a^{2}-1-a^{4}-1.
\frac{-2}{a^{2}-1}
Expand \left(a-1\right)\left(a+1\right).
a^{2}+1-\frac{a^{4}+1}{\left(a-1\right)\left(a+1\right)}
Factor a^{2}-1.
\frac{\left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{a^{4}+1}{\left(a-1\right)\left(a+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2}+1 times \frac{\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}.
\frac{\left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)-\left(a^{4}+1\right)}{\left(a-1\right)\left(a+1\right)}
Since \frac{\left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} and \frac{a^{4}+1}{\left(a-1\right)\left(a+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a^{4}-a^{2}+a^{2}-1-a^{4}-1}{\left(a-1\right)\left(a+1\right)}
Do the multiplications in \left(a^{2}+1\right)\left(a-1\right)\left(a+1\right)-\left(a^{4}+1\right).
\frac{-2}{\left(a-1\right)\left(a+1\right)}
Combine like terms in a^{4}-a^{2}+a^{2}-1-a^{4}-1.
\frac{-2}{a^{2}-1}
Expand \left(a-1\right)\left(a+1\right).
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Simultaneous equation
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Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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