Evaluate
\frac{2m}{\left(b+1\right)\left(b+2\right)}
Factor
\frac{2m}{\left(b+1\right)\left(b+2\right)}
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\frac{2m\left(b+2\right)}{\left(b+1\right)\left(b+2\right)}-\frac{2m\left(b+1\right)}{\left(b+1\right)\left(b+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b+1 and b+2 is \left(b+1\right)\left(b+2\right). Multiply \frac{2m}{b+1} times \frac{b+2}{b+2}. Multiply \frac{2m}{b+2} times \frac{b+1}{b+1}.
\frac{2m\left(b+2\right)-2m\left(b+1\right)}{\left(b+1\right)\left(b+2\right)}
Since \frac{2m\left(b+2\right)}{\left(b+1\right)\left(b+2\right)} and \frac{2m\left(b+1\right)}{\left(b+1\right)\left(b+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2mb+4m-2mb-2m}{\left(b+1\right)\left(b+2\right)}
Do the multiplications in 2m\left(b+2\right)-2m\left(b+1\right).
\frac{2m}{\left(b+1\right)\left(b+2\right)}
Combine like terms in 2mb+4m-2mb-2m.
\frac{2m}{b^{2}+3b+2}
Expand \left(b+1\right)\left(b+2\right).
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Limits
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