Answer
$x+3$
Work Step by Step
... When one denominator is the opposite, or additive inverse of the other,
first multiply either rational expression by $\displaystyle \frac{-1}{-1}$
to obtain a common denominator.
$\displaystyle \frac{x^{2}}{x-3}+\frac{9}{3-x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{x^{2}}{x-3}+ \frac{-9}{x-3}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and
place the sum/difference over the common denominator.
If possible, factor and simplify the result.
$= \displaystyle \frac{x^{2}-9}{x-3}$
... recognize a difference of squares in the numerator
$= \displaystyle \frac{(x+3)(x-3)}{(x-3)}$
... reduce (divide the numerator and denominator with common factors)
$=\displaystyle \frac{x+3}{1}$
$=x+3$
