Answer
$\dfrac{3}{x - 6}$
Work Step by Step
Do the subtraction in the denominator first.
Find the least common denominator (LCD) of the two terms of the denominator and convert whole numbers to fractions:
$\dfrac{\frac{3}{x - 4}}{\frac{x - 4}{x - 4} - \frac{2}{x - 4}}$
Perform the subtraction in the denominator:
$=\dfrac{\frac{3}{x - 4}}{\frac{x - 4-2}{x - 4}}$
$=\dfrac{\frac{3}{x - 4}}{\frac{x - 6}{x - 4}}$
Rewrite this fraction as a division problem:
$=\dfrac{3}{x - 4} \div \dfrac{x - 6}{x - 4}$
To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction:
$=\dfrac{3}{x - 4} \cdot \dfrac{x - 4}{x - 6}$
Multiply numerator with numerator and denominator with denominator:
$=\dfrac{3(x - 4)}{(x - 4)(x - 6)}$
Cancel common terms in the numerator and denominator:
$=\dfrac{3}{x - 6}$