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\frac{3b-39}{\left(b-5\right)\left(b-2\right)}-\frac{3}{b-2}
Factor b^{2}-7b+10.
\frac{3b-39}{\left(b-5\right)\left(b-2\right)}-\frac{3\left(b-5\right)}{\left(b-5\right)\left(b-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b-5\right)\left(b-2\right) and b-2 is \left(b-5\right)\left(b-2\right). Multiply \frac{3}{b-2} times \frac{b-5}{b-5}.
\frac{3b-39-3\left(b-5\right)}{\left(b-5\right)\left(b-2\right)}
Since \frac{3b-39}{\left(b-5\right)\left(b-2\right)} and \frac{3\left(b-5\right)}{\left(b-5\right)\left(b-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3b-39-3b+15}{\left(b-5\right)\left(b-2\right)}
Do the multiplications in 3b-39-3\left(b-5\right).
\frac{-24}{\left(b-5\right)\left(b-2\right)}
Combine like terms in 3b-39-3b+15.
\frac{-24}{b^{2}-7b+10}
Expand \left(b-5\right)\left(b-2\right).
\frac{3b-39}{\left(b-5\right)\left(b-2\right)}-\frac{3}{b-2}
Factor b^{2}-7b+10.
\frac{3b-39}{\left(b-5\right)\left(b-2\right)}-\frac{3\left(b-5\right)}{\left(b-5\right)\left(b-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b-5\right)\left(b-2\right) and b-2 is \left(b-5\right)\left(b-2\right). Multiply \frac{3}{b-2} times \frac{b-5}{b-5}.
\frac{3b-39-3\left(b-5\right)}{\left(b-5\right)\left(b-2\right)}
Since \frac{3b-39}{\left(b-5\right)\left(b-2\right)} and \frac{3\left(b-5\right)}{\left(b-5\right)\left(b-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3b-39-3b+15}{\left(b-5\right)\left(b-2\right)}
Do the multiplications in 3b-39-3\left(b-5\right).
\frac{-24}{\left(b-5\right)\left(b-2\right)}
Combine like terms in 3b-39-3b+15.
\frac{-24}{b^{2}-7b+10}
Expand \left(b-5\right)\left(b-2\right).