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

Algebra ->  Polynomials-and-rational-expressions -> 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       Log On


   

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) About Me  (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) About Me  (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:
%28y-6%29+%2F+%28y-9%29+-+%28y%2B1%29+%2F+%28y%2B9%29+%2B+%28y-63%29+%2F+%28y%5E2+-+81%29
you can factor the y%5E2+-+81 to get %28y-9%29%2A%28y%2B9%29%29
this makes your expression equal to:

you are correct in that the common denominator will be %28y-9%29%2A%28y%2B9%29.
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:
%28y%5E2+%2B+3y+-+54+-+y%5E2+%2B+8y+%2B+9+%2B+y+-+63%29+%2F+%28%28y-9%29%2A%28y%2B9%29%29
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:
%2812y+-+108%29+%2F+%28%28y-9%29%2A%28y%2B9%29%29
you would now simplify this further by factoring your numerator to get:
%2812%2A%28y-9%29%29+%2F+%28%28y-9%29%2A%28y%2B9%29%29
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%2F%28y%2B9%29
that's your answer since you can't simplify it any further.