(1 - $\dfrac{x-3√x}{x-9}$ $)$ : ($\dfrac{√x-3}{2-√x}$ + $\dfrac{√x-2}{3+√x}$ - $\dfrac{9-x}{x+√x-6}$ )
= (1 - $\dfrac{√x(√x-3)}{(√x-3)(√x+3)}$ ) : ($\dfrac{3-√x}{√x-2}$ + $\dfrac{√x-2}{√x+3}$ - $\dfrac{9-x}{(√x-2)(√x+3)}$
= (1 - $\dfrac{√x}{√x+3}$ ) : ($\dfrac{(3-√x)(√x+3)}{(√x-2)(√x+3)}$ + $\dfrac{(√x-2)(√x-2)}{(√x-2)(√x+3)}$ - $\dfrac{9-x}{(√x-2)(√x+3)}$
= (1 - $\dfrac{√x}{√x+3}$ ) : ($\dfrac{9-x}{(√x-2)(√x+3)}$ + $\dfrac{x-4√x+4}{(√x-2)(√x+3)}$ - $\dfrac{9-x}{(√x-2)(√x+3)}$
= (1 - $\dfrac{√x}{√x+3}$ ) : $\dfrac{9-x+x-4√x+4-9+x}{(√x-2)(√x+3)}$
= (1 - $\dfrac{√x}{√x+3}$ ) : $\dfrac{x-4√x+4}{(√x-2)(√x+3)}$
= $\dfrac{√x+3-√x}{√x+3}$ : $\dfrac{(√x-2)^2}{(√x-2)(√x+3)}$
= $\dfrac{3}{√x+3}$ : $\dfrac{√x-2}{√x+3}$
= $\dfrac{3}{√x+3}$ . $\dfrac{√x+3}{√x-2}$
= $\dfrac{3}{√x-2}$
