Evaluate
\frac{1}{\left(x-4\right)\left(x-3\right)}
Expand
\frac{1}{x^{2}-7x+12}
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\frac{3}{\left(x-4\right)\left(x-3\right)}-\frac{2}{\left(x-4\right)\left(x-3\right)}
Factor x^{2}-7x+12.
\frac{1}{\left(x-4\right)\left(x-3\right)}
Since \frac{3}{\left(x-4\right)\left(x-3\right)} and \frac{2}{\left(x-4\right)\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 3 to get 1.
\frac{1}{x^{2}-7x+12}
Expand \left(x-4\right)\left(x-3\right).
\frac{3}{\left(x-4\right)\left(x-3\right)}-\frac{2}{\left(x-4\right)\left(x-3\right)}
Factor x^{2}-7x+12.
\frac{1}{\left(x-4\right)\left(x-3\right)}
Since \frac{3}{\left(x-4\right)\left(x-3\right)} and \frac{2}{\left(x-4\right)\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 3 to get 1.
\frac{1}{x^{2}-7x+12}
Expand \left(x-4\right)\left(x-3\right).
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