Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 580: 19

$= \frac{(x-11)(x+9)}{(x-4)^{2}} $

$\frac{x^{2}-16x+55}{x^{2}-x-12} \times \frac{x^{2}+12x+27}{x^{2}-9x+20}$ $= \frac{(x-5)(x-11)}{(x-4)(x+3)} \times \frac{(x+9)(x+3)}{(x-4)(x-5)}$ $= \frac{(x-5)(x-11)(x+9)(x+3)}{(x-4)(x+3)(x-4)(x-5)} $ $= \frac{(x-11)(x+9)(x+3)}{(x-4)(x+3)(x-4)} $ $= \frac{(x-11)(x+9)}{(x-4)(x-4)} $ $= \frac{(x-11)(x+9)}{(x-4)^{2}} $