## Algebra: A Combined Approach (4th Edition)

$2x-3$
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, $\frac{(2x-3)(x+2)}{x+2}=2x-3$.