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\frac{1}{2a+1}+\frac{1}{a-\left(b+1\right)}
Combine a and a to get 2a.
\frac{-\left(b+1\right)+a}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}+\frac{2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a+1 and a-\left(b+1\right) is \left(2a+1\right)\left(-\left(b+1\right)+a\right). Multiply \frac{1}{2a+1} times \frac{-\left(b+1\right)+a}{-\left(b+1\right)+a}. Multiply \frac{1}{a-\left(b+1\right)} times \frac{2a+1}{2a+1}.
\frac{-\left(b+1\right)+a+2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
Since \frac{-\left(b+1\right)+a}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)} and \frac{2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)} have the same denominator, add them by adding their numerators.
\frac{-b-1+a+2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
Do the multiplications in -\left(b+1\right)+a+2a+1.
\frac{-b+3a}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
Combine like terms in -b-1+a+2a+1.
\frac{-b+3a}{2a^{2}-2ab-a-b-1}
Expand \left(2a+1\right)\left(-\left(b+1\right)+a\right).
\frac{1}{2a+1}+\frac{1}{a-\left(b+1\right)}
Combine a and a to get 2a.
\frac{-\left(b+1\right)+a}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}+\frac{2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a+1 and a-\left(b+1\right) is \left(2a+1\right)\left(-\left(b+1\right)+a\right). Multiply \frac{1}{2a+1} times \frac{-\left(b+1\right)+a}{-\left(b+1\right)+a}. Multiply \frac{1}{a-\left(b+1\right)} times \frac{2a+1}{2a+1}.
\frac{-\left(b+1\right)+a+2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
Since \frac{-\left(b+1\right)+a}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)} and \frac{2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)} have the same denominator, add them by adding their numerators.
\frac{-b-1+a+2a+1}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
Do the multiplications in -\left(b+1\right)+a+2a+1.
\frac{-b+3a}{\left(2a+1\right)\left(-\left(b+1\right)+a\right)}
Combine like terms in -b-1+a+2a+1.
\frac{-b+3a}{2a^{2}-2ab-a-b-1}
Expand \left(2a+1\right)\left(-\left(b+1\right)+a\right).