SOLUTION: divide and simplify. Please help me solve. v^2+3v/v^2+2V-3 DIVIDED BY v/v+1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: divide and simplify. Please help me solve. v^2+3v/v^2+2V-3 DIVIDED BY v/v+1      Log On


   

Question 251531: divide and simplify.
Please help me solve.
v^2+3v/v^2+2V-3 DIVIDED BY v/v+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28v%5E2%2B3v%29%2F%28v%5E2%2B2v-3%29%29%2F%28%28v%29%2F%28v%2B1%29%29 Start with the given expression.


%28%28v%5E2%2B3v%29%2F%28v%5E2%2B2v-3%29%29%28%28v%2B1%29%2F%28v%29%29 Multiply the first fraction %28v%5E2%2B3v%29%2F%28v%5E2%2B2v-3%29 by the reciprocal of the second fraction %28v%29%2F%28v%2B1%29.


%28%28v%28v%2B3%29%29%2F%28v%5E2%2B2v-3%29%29%28%28v%2B1%29%2F%28v%29%29 Factor v%5E2%2B3v to get v%2A%28v%2B3%29.


%28%28v%28v%2B3%29%29%2F%28%28v%2B3%29%28v-1%29%29%29%28%28v%2B1%29%2F%28v%29%29 Factor v%5E2%2B2v-3 to get %28v%2B3%29%2A%28v-1%29.


%28v%28v%2B3%29%28v%2B1%29%29%2F%28v%28v%2B3%29%28v-1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28v%2B1%29%2F%28v-1%29 Simplify.


So %28%28v%5E2%2B3v%29%2F%28v%5E2%2B2v-3%29%29%2F%28%28v%29%2F%28v%2B1%29%29 simplifies to %28v%2B1%29%2F%28v-1%29.


In other words,