#### Answer

$2x-3$

#### Work Step by Step

Step 1: $\frac{2x^{2}+5x}{x+2}-\frac{4x+6}{x+2}$
Step 2: $\frac{2x^{2}+5x-(4x+6)}{x+2}$
Step 3: $\frac{2x^{2}+5x-4x-6}{x+2}$
Step 4: $\frac{2x^{2}+x-6}{x+2}$
Step 5: $\frac{2x^{2}-3x+4x-6}{x+2}$
Step 6: $\frac{x(2x-3)+2(2x-3)}{x+2}$
Step 7: $\frac{(2x-3)(x+2)}{x+2}$
Step 8: Eliminating (x+2) as it is common to both the numerator and the denominator,
$\frac{(2x-3)(x+2)}{x+2}=2x-3$.