Answer
$\displaystyle \frac{x}{x-6}$
Work Step by Step
To subtract rational expressions with the same denominator,
subtract numerators and place the difference over the common denominator.
If possible, factor and simplify the result.
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Don't forget to place the second numerator in parentheses when subtracting.
$\displaystyle \frac{2x+3}{3x-6}-\frac{3-x}{3x-6}= \displaystyle \frac{2x+3-(3-x)}{3x-6}$
$= \displaystyle \frac{2x+3-3+x}{3x-6}$
$= \displaystyle \frac{3x}{3x-6}$
$=\displaystyle \frac{3(x)}{3(x-6)}$
... reduce (divide the numerator and denominator with common factors)
$=\displaystyle \frac{x}{x-6}$
