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\frac{1}{x-3}+\frac{2}{4\left(x-3\right)}
Factor 4x-12.
\frac{4}{4\left(x-3\right)}+\frac{2}{4\left(x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 4\left(x-3\right) is 4\left(x-3\right). Multiply \frac{1}{x-3} times \frac{4}{4}.
\frac{6}{4\left(x-3\right)}
Since \frac{4}{4\left(x-3\right)} and \frac{2}{4\left(x-3\right)} have the same denominator, add them by adding their numerators. Add 4 and 2 to get 6.
\frac{6}{4x-12}
Expand 4\left(x-3\right).