SOLUTION: Hi! This question has been bugging me since I first looked at it, because it leaves me confused as to where to start. I want to believe that you factor the denominators, but I have

Algebra ->  Rational-functions -> SOLUTION: Hi! This question has been bugging me since I first looked at it, because it leaves me confused as to where to start. I want to believe that you factor the denominators, but I have      Log On


   

Question 175922: Hi! This question has been bugging me since I first looked at it, because it leaves me confused as to where to start. I want to believe that you factor the denominators, but I have never been too great at factoring and am not sure if anything I'm doing is right! Thanks in advance.
Simplify.
+%28-7v%29%2F%282u%5E2-5uv-3v%5E2%29+-+1%2F%283v-u%29+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+%28-7v%29%2F%282u%5E2-5uv-3v%5E2%29+-+1%2F%283v-u%29+ Start with the given expression.


+%28-7v%29%2F%28-%28v%2B2u%29%283v-u%29%29+-+1%2F%283v-u%29+ Factor the first denominator


+%287v%29%2F%28%28v%2B2u%29%283v-u%29%29+-+1%2F%283v-u%29+ Reduce


Take note that the LCD is %28v%2B2u%29%283v-u%29


+%287v%29%2F%28%28v%2B2u%29%283v-u%29%29+-+%28v%2B2u%29%2F%28%28v%2B2u%29%283v-u%29%29+ Multiply the the numerator and denominator of the second fraction by %28v%2B2u%29%2F%28v%2B2u%29 (to get the denominator equal to the LCD)


+%287v-%28v%2B2u%29%29%2F%28%28v%2B2u%29%283v-u%29%29+ Combine the fractions. This is now possible since the denominators are equal.


+%287v-v-2u%29%2F%28%28v%2B2u%29%283v-u%29%29+ Distribute


+%286v-2u%29%2F%28%28v%2B2u%29%283v-u%29%29+ Combine like terms.


+%282%283v-u%29%29%2F%28%28v%2B2u%29%283v-u%29%29+ Factor out the GCF 2 from the numerator


+%282%2Ahighlight%28%283v-u%29%29%29%2F%28%28v%2B2u%29highlight%28%283v-u%29%29%29+ Highlight the common terms.


+%282%2Across%28%283v-u%29%29%29%2F%28%28v%2B2u%29cross%28%283v-u%29%29%29+ Cancel out the common terms.


2%2F%28v%2B2u%29 Simplify



So +%28-7v%29%2F%282u%5E2-5uv-3v%5E2%29+-+1%2F%283v-u%29+ simplifies to 2%2F%28v%2B2u%29