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## Polynomial Factoring

A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.

# Simplifying Rational Expressions

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

If $\frac{x+2}{x^2+5x-6} \times \frac{x^2-6x+5}{3x+6} = \frac{x-c}{ax+b},$ where $$a$$, $$b$$ and $$c$$ are constants, what is $$a+b+c$$?

If $\frac{35x^{4}y^{3}}{3a^{8}b^{7}} \div \frac{5x^{6}y^{5}}{21a^{9}b^{8}} = \frac{pab}{x^my^n},$ where $$p$$, $$m$$ and $$n$$ are constants, what is the value of $$p+m+n$$?

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 $$a$$?

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