Algebra
# Polynomial Factoring

Simplify $\frac{x^2+11x+18}{x+2} \div \frac{x+9}{12}.$

(For all these problems you can automatically assume only values of $x$ which do not cause division by zero are used.)

Simplify $\frac{4x^2+20x+21}{3x+6} \times \frac{2x+3}{2x+7} \div \frac{4x^2+12x+9}{6x+12}.$

If $\frac{x}{x-7}-\frac{x}{x+9}=\frac{ax}{(x-7)(x+9)},$

holds for all values of $x$, what is the value of $a$?