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Differentiate w.r.t. a
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\frac{1}{a-b}-\frac{b}{\left(a+b\right)\left(a-b\right)}
Factor a^{2}-b^{2}.
\frac{a+b}{\left(a+b\right)\left(a-b\right)}-\frac{b}{\left(a+b\right)\left(a-b\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-b and \left(a+b\right)\left(a-b\right) is \left(a+b\right)\left(a-b\right). Multiply \frac{1}{a-b} times \frac{a+b}{a+b}.
\frac{a+b-b}{\left(a+b\right)\left(a-b\right)}
Since \frac{a+b}{\left(a+b\right)\left(a-b\right)} and \frac{b}{\left(a+b\right)\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a}{\left(a+b\right)\left(a-b\right)}
Combine like terms in a+b-b.
\frac{a}{a^{2}-b^{2}}
Expand \left(a+b\right)\left(a-b\right).