Perform the indicated operations and simplify

[Gr8fu13]

Perform the indicated operations and simplify. Here is what I have done:

(y-5)/(y-9)-(y+1)/(y+9)+(y-81)/(y^2-81)<-----original problem
(y-5)/(y-9)-(y+1)/(y+9)+(y-81)/((y+9)(y-9))
(y-5)/(y-9)×(y+9)/(y+9)-(y+1)/(y+9)×(y-9)/(y-9)+(y-81)/((y+9)(y-9))
(y^2-45y)/((y+9)(y-9))-(y^2-9y)/((y+9)(y-9))+(y-81)/((y+9)(y-9))
(y^2-45y-y^2-9y+y-81)/((y+9)(y-9))
(-54y^2-81)/((y+9)(y-9))<-----Answer
Or would it be:
(-54y+y-81)/((y+9)(y-9))

I wish I could attach a microsoft word document, much easier to understand the way I have it written in there

 

[soroban]

Hello, Gr8fu13!

Perform the indicated operations and simplify.
Here is what I have done:

. . \(\displaystyle \frac{y-5}{y-9} - \frac{y+1}{y+9} + \frac{y-81}{y^2-81}\)

. . \(\displaystyle =\;\frac{y-5}{y-9} - \frac{y+1}{y+9} + \frac{y-81}{(y+9)(y-9)}\) . Yes!

. . \(\displaystyle =\;\frac{y-5}{y-9}\cdot\frac{y+9}{y+9} - \frac{y+1}{y+9}\cdot\frac{y-9}{y-9} + \frac{y-81}{(y+9)(y-9)}\) . Right!

. . \(\displaystyle =\;\frac{y^2-45y}{(y+9)(y-9)} - \frac{y^2-9y}{(y+9)(y-9)} + \frac{y-81}{(y+9)(y-9)}\) . You mutliplied incorrectly!

\(\displaystyle \text{You have: }\:\frac{(y-5)(y+9)}{(y-9)(y+9)} - \frac{(y+1)(y-9)}{(y-9)(y+9)} + \frac{y-81}{(y-9)(y+9)}\)

. . . . . . \(\displaystyle =\;\frac{(y^2 +4y - 45) - (y^2 - 8y - 9) + (y-81)}{(y-9)(y+9)}\)

. . . . . . \(\displaystyle =\;\frac{y^2 + 4y - 45 - y^2 + 8y + 9 + y - 81}{(y-9)(y+9)}\)

. . . . . . \(\displaystyle =\;\frac{13y - 117}{(y-9)(y+9)}\)

. . . . . . \(\displaystyle =\;\frac{13(y - 9)}{(y-9)(y+9)}\)

. . . . . . \(\displaystyle =\;\frac{13}{y+9}\)

 

[mmm4444bot]

I wish I could attach a microsoft word document

:idea: You can attach a screenshot

It's nice that soroban pointed out the error and location. Too bad he didn't give the poster a chance to learn something, by stopping there.