SOLUTION: Can someone please help me with multiplying rational expressions. Here are a couple of expressions I am working on. 3/ a^2 + a * 2a + 2/ 6 w^2 -1/ (w-1)^2 * w-1/ w^2 + 2w + 1

Algebra ->  Rational-functions -> SOLUTION: Can someone please help me with multiplying rational expressions. Here are a couple of expressions I am working on. 3/ a^2 + a * 2a + 2/ 6 w^2 -1/ (w-1)^2 * w-1/ w^2 + 2w + 1      Log On


   

Question 224739: Can someone please help me with multiplying rational expressions. Here are a couple of expressions I am working on.
3/ a^2 + a * 2a + 2/ 6
w^2 -1/ (w-1)^2 * w-1/ w^2 + 2w + 1

Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


%28%283%29%2F%28a%5E2%2Ba%29%29%28%282a%2B2%29%2F%286%29%29 Start with the given expression.


%28%283%29%2F%28a%28a%2B1%29%29%29%28%282a%2B2%29%2F%286%29%29 Factor a%5E2%2Ba to get a%28a%2B1%29.


%28%283%29%2F%28a%28a%2B1%29%29%29%28%282%28a%2B1%29%29%2F%286%29%29 Factor 2a%2B2 to get 2%28a%2B1%29.


%28%283%29%2F%28a%28a%2B1%29%29%29%28%282%28a%2B1%29%29%2F%282%2A3%29%29 Factor 6 to get 2%2A3.


%283%2A2%28a%2B1%29%29%2F%28a%2A%28a%2B1%29%282%2A3%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1%2Fa Simplify.


So %28%283%29%2F%28a%5E2%2Ba%29%29%28%282a%2B2%29%2F%286%29%29 simplifies to 1%2Fa.


In other words, %28%283%29%2F%28a%5E2%2Ba%29%29%28%282a%2B2%29%2F%286%29%29=1%2Fa where a%3C%3E0 or a%3C%3E-1





# 2




%28%28w%5E2-1%29%2F%28%28w-1%29%5E2%29%29%28%28w-1%29%2F%28w%5E2%2B2w%2B1%29%29 Start with the given expression.


Factor w%5E2-1 to get %28w-1%29%2A%28w%2B1%29.


Break up %28w-1%29%5E2 to get %28w-1%29%28w-1%29.


Factor w%5E2%2B2w%2B1 to get %28w%2B1%29%28w%2B1%29.


%28%28w-1%29%2A%28w%2B1%29%28w-1%29%29%2F%28%28w-1%29%28w-1%29%28w%2B1%29%28w%2B1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1%2F%28w%2B1%29 Simplify.


So %28%28w%5E2-1%29%2F%28%28w-1%29%5E2%29%29%28%28w-1%29%2F%28w%5E2%2B2w%2B1%29%29 simplifies to 1%2F%28w%2B1%29.


In other words,