Answer
$\displaystyle \frac{5x+5}{x-3}$
Work Step by Step
To add rational expressions with the same denominator,
add numerators and place the sum over the common denominator.
If possible, factor and simplify the result.
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$\displaystyle \frac{x}{x-3}+\frac{4x+5}{x-3} = \displaystyle \frac{x+4x+5}{x-3}$
$= \displaystyle \frac{5x+5}{x-3}$
$= \displaystyle \frac{5(x+1)}{x-3}\qquad$... no common factors to reduce by