Solve for: (2x^2+11x+15)/(x^2+6x+9)

Expression: $\frac{2x^{2}+11x+15}{x^{2}+6x+9}$

Factor $2x^{2}+11x+15:{\quad}(2x+5)(x+3)$

$=\frac{(2x+5)(x+3)}{x^{2}+6x+9}$

Factor $x^{2}+6x+9:{\quad}(x+3)^{2}$

$=\frac{(2x+5)(x+3)}{(x+3)^{2}}$

Apply exponent rule $a^{b+c}=a^b\cdot a^c$

$=\frac{(2x+5)(x+3)}{(x+3)(x+3)}$

Cancel the common factor: $ x+3$

$=\frac{2x+5}{x+3}$