SOLUTION: Please help! Perform the indicated operations and simplify v-7/v-9 - v+1/v+9 + v-45/v^2-81

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Question 315558: Please help!
Perform the indicated operations and simplify
v-7/v-9 - v+1/v+9 + v-45/v^2-81
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%29 Start with the given expression.


Factor the last denominator.


Take note that the LCD is %28v-9%29%28v%2B9%29


Multiply the first fraction by %28v%2B9%29%2F%28v%2B9%29 to get that denominator to equal the LCD.


Combine the fractions.


FOIL the numerator of the first fraction.


Multiply the second fraction by %28v-9%29%2F%28v-9%29 to get that denominator to equal the LCD.


Combine the fractions.


FOIL the numerator of the second fraction.


Now the denominators are all equal to the LCD, we can finally combine the three fractions.


%28%28v%5E2%2B2v-63%29-+%28v%5E2-8v-9%29%2B+%28v-45%29%29%2F%28%28v-9%29%28v%2B9%29%29 Combine the three fractions by placing the numerators all over the LCD.


%28v%5E2%2B2v-63-+v%5E2%2B8v%2B9%2Bv-45%29%2F%28%28v-9%29%28v%2B9%29%29 Distribute.


%2811v-99%29%2F%28%28v-9%29%28v%2B9%29%29 Combine like terms.


%2811%28v-9%29%29%2F%28%28v-9%29%28v%2B9%29%29 Factor the numerator.


%2811%2Ahighlight%28%28v-9%29%29%29%2F%28highlight%28%28v-9%29%29%28v%2B9%29%29 Highlight the common terms.


%2811%2Across%28%28v-9%29%29%29%2F%28cross%28%28v-9%29%29%28v%2B9%29%29 Cancel out the common terms.


11%2F%28v%2B9%29 Simplify.


So %28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%29 simplifies to 11%2F%28v%2B9%29


In other words, where v%3C%3E-9 or v%3C%3E9