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\frac{1}{b-3}+\frac{3}{4\left(b-3\right)}
Factor 4b-12.
\frac{4}{4\left(b-3\right)}+\frac{3}{4\left(b-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-3 and 4\left(b-3\right) is 4\left(b-3\right). Multiply \frac{1}{b-3} times \frac{4}{4}.
\frac{7}{4\left(b-3\right)}
Since \frac{4}{4\left(b-3\right)} and \frac{3}{4\left(b-3\right)} have the same denominator, add them by adding their numerators. Add 4 and 3 to get 7.
\frac{7}{4b-12}
Expand 4\left(b-3\right).