SOLUTION: Perform the indicated operations and simplify. <pre> y-6 y+1 y-63 ----- - ----- + ----- y-9 y+9 y^2-81 </pre> I have gotten this far, but

Question 587716: Perform the indicated operations and simplify.

y-6 y+1 y-63 ----- - ----- + ----- y-9 y+9 y^2-81

I have gotten this far, but don't think it is right.
The LCD is (y-9)(y+9)
Long story short, after all of the "factoring" I did, the end result came out to be
25y+63
------
(y-9)(y+9)
My only question now is what do I do with the third part of the equation?
y-63
-----
y^2-81
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Perform the indicated operations and simplify.
y-6 y+1 y-63
----- - -----
y-9 y+9 y^2-81
--------------------
Rewrite each fraction with the lcd as its denominator:
[(y-6)(y+9]/lcd - [(y+1)(y-9)]/lcd + (y-63)/lcd
------
Combine the numerators over the lcd:
----
= [y^2+3y-45 - (y^2-8y-9) + (y-63)]/lcd
-----
Simplify:
= [3y+8y+y-45+9-63]/lcd
----------------------------
= [12y-99]/lcd
-----
= [12y-99]/[y^2-81]
=======================
Cheers,
Stan H.
=======================

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i don't think you did the arithmetic correctly.
i wound up with 12 / (y+9)
here's how.
your expression is:

you can factor the to get
this makes your expression equal to:

you are correct in that the common denominator will be .
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:

you can now combine everything under the same common denominator to get:

you would now simplify your numerator by multiplying out the factors to get:

you would simplify your numerator further by combining like terms to get:

you would now simplify your numerator further by removing parentheses to get:

you would now simplify your numerator further by grouping like terms to get:

you would now simplify your numerator further by combining like terms to get:

you would now simplify this further by factoring your numerator to get:

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:

that's your answer since you can't simplify it any further.

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