Evaluate
\frac{2b}{4b^{2}-1}
Factor
\frac{2b}{4b^{2}-1}
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\frac{b\left(2b+1\right)}{\left(2b-1\right)\left(2b+1\right)}-\frac{b\left(2b-1\right)}{\left(2b-1\right)\left(2b+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2b-1 and 2b+1 is \left(2b-1\right)\left(2b+1\right). Multiply \frac{b}{2b-1} times \frac{2b+1}{2b+1}. Multiply \frac{b}{2b+1} times \frac{2b-1}{2b-1}.
\frac{b\left(2b+1\right)-b\left(2b-1\right)}{\left(2b-1\right)\left(2b+1\right)}
Since \frac{b\left(2b+1\right)}{\left(2b-1\right)\left(2b+1\right)} and \frac{b\left(2b-1\right)}{\left(2b-1\right)\left(2b+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2b^{2}+b-2b^{2}+b}{\left(2b-1\right)\left(2b+1\right)}
Do the multiplications in b\left(2b+1\right)-b\left(2b-1\right).
\frac{2b}{\left(2b-1\right)\left(2b+1\right)}
Combine like terms in 2b^{2}+b-2b^{2}+b.
\frac{2b}{4b^{2}-1}
Expand \left(2b-1\right)\left(2b+1\right).
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