Answer
$-\dfrac{2x^{2}-14x-55}{(x+7)(x+2)(x+3)}$
Work Step by Step
$\dfrac{9}{x^{2}+9x+14}-\dfrac{3x}{x^{2}+10x+21}+\dfrac{x+4}{x^{2}+5x+6}$
Factor all three rational expressions completely:
$\dfrac{9}{(x+7)(x+2)}-\dfrac{3x}{(x+7)(x+3)}+\dfrac{x+4}{(x+3)(x+2)}=...$
Evaluate the indicated operations and simplify:
$...=\dfrac{9(x+3)-3x(x+2)+(x+4)(x+7)}{(x+7)(x+2)(x+3)}=...$
$...=\dfrac{9x+27-3x^{2}-6x+x^{2}+11x+28}{(x+7)(x+2)(x+3)}=...$
$...=\dfrac{-2x^{2}+14x+55}{(x+7)(x+2)(x+3)}=-\dfrac{2x^{2}-14x-55}{(x+7)(x+2)(x+3)}$
