Question 317267
Use the common denominator, {{{w^2-81=(w-9)(w+9)}}}
.
.

{{{(w-8)/(w-9) - (w+1)/(w+9) + (w-27)/(w^2-81)=((w-8)(w+9))/((w-9)(w+9)) - ((w+1)(w-9))/((w-9)(w+9)) + (w-27)/(w^2-81)}}}
{{{(w-8)/(w-9) - (w+1)/(w+9) + (w-27)/(w^2-81)=((w^2+w-72)-(w^2-8w-9)+(w-27))/(w^2-81)}}}
{{{(w-8)/(w-9) - (w+1)/(w+9) + (w-27)/(w^2-81)=(10w-90)/(w^2-81)}}}
{{{(w-8)/(w-9) - (w+1)/(w+9) + (w-27)/(w^2-81)=(10(w-9))/((w-9)(w+9))}}}
{{{(w-8)/(w-9) - (w+1)/(w+9) + (w-27)/(w^2-81)=highlight(10/(w+9))}}}