Question 587716
i don't think you did the arithmetic correctly.
i wound up with 12 / (y+9)
here's how.

your expression is:
{{{(y-6) / (y-9) - (y+1) / (y+9) + (y-63) / (y^2 - 81)}}}
you can factor the {{{y^2 - 81}}} to get {{{(y-9)*(y+9))}}}
this makes your expression equal to:
{{{(y-6) / (y-9) - (6+1) / (y+9) + (y-63) / ((y-9)*(y+9))}}}
you are correct in that the common denominator will be {{{(y-9)*(y+9)}}}.
you multiply the first term in the expression by (y+9) and you multiply the second term in the expresion by (y-9) to get:
{{{((y-6)*(y+9))/((y-9)*(y+9)) - ((y+1)*(y-9))/((y-9)*(y+9)) + (y-63)/((y-9)*(y+9))}}}
you can now combine everything under the same common denominator to get:
{{{((y-6)*(y+9) - (y+1)*(y-9) + (y-63))/((y-9)*(y+9))}}}
you would now simplify your numerator by multiplying out the factors to get:
{{{((y^2 + 9y - 6y - 54) - (y^2 - 9y + y - 9) + (y - 63)) / ((y-9)*(y+9))}}}
you would simplify your numerator further by combining like terms to get:
{{{(y^2 + 3y - 54) - (y^2 - 8y - 9) + (y - 63)) / ((y-9)*(y+9))}}}
you would now simplify your numerator further by removing parentheses to get:
{{{(y^2 + 3y - 54 - y^2 + 8y + 9 + y - 63) / ((y-9)*(y+9))}}}
you would now simplify your numerator further by grouping like terms to get:
{{{((y^2 - y^2) + (3y + 8y + y) - (54 - 9 + 63)) / ((y-9)*(y+9))}}}
you would now simplify your numerator further by combining like terms to get:
{{{(12y - 108) / ((y-9)*(y+9))}}}
you would now simplify this further by factoring your numerator to get:
{{{(12*(y-9)) / ((y-9)*(y+9))}}}
you would now simplify this further by canceling out the common terms of (y-9) in the numerator and (y-9) in the denominator to get:
{{{12/(y+9)}}}
that's  your answer since you can't simplify it any further.