Answer
$=\displaystyle \frac{x+12}{x(x+3)}, \quad x\neq-3,0$
Work Step by Step
The denominators are different.
Find a common denominator.
LCD=$x(x+3)$
$\displaystyle \frac{4}{x}-\frac{3}{x+3}=\frac{4(x+3)}{x(x+3)}-\frac{3x}{x(x+3)}$
$=\displaystyle \frac{4x+12-3x}{x(x+3)}$
$=\displaystyle \frac{x+12}{x(x+3)}$
... exclude values that yield 0 in the denominator:
$x\neq-3,0$
... and, cancel common factors (here, there are none)
$=\displaystyle \frac{x+12}{x(x+3)}, \quad x\neq-3,0$
