Answer
$\dfrac{x^{2}+9x+20}{x^{2}-15x+44}\cdot\dfrac{x^{2}-11x+28}{x^{2}+12x+35}=\dfrac{(x+4)(x-7)}{(x-11)(x+7)}$
Work Step by Step
$\dfrac{x^{2}+9x+20}{x^{2}-15x+44}\cdot\dfrac{x^{2}-11x+28}{x^{2}+12x+35}$
Factor both rational expression completely:
$\dfrac{(x+5)(x+4)}{(x-4)(x-11)}\cdot\dfrac{(x-4)(x-7)}{(x+7)(x+5)}=...$
Multiply the two expressions and simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{(x+5)(x+4)(x-4)(x-7)}{(x-4)(x-11)(x+7)(x+5)}=\dfrac{(x+4)(x-7)}{(x-11)(x+7)}$
