SOLUTION: I am trying to finish a problem where I am multiplying rational expressions. This is what I have simplified it down to: (c-1)*(2c+1)/(c^(2)-1). I know I must factor out (c-1) and (

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am trying to finish a problem where I am multiplying rational expressions. This is what I have simplified it down to: (c-1)*(2c+1)/(c^(2)-1). I know I must factor out (c-1) and (      Log On


   

Question 597877: I am trying to finish a problem where I am multiplying rational expressions. This is what I have simplified it down to: (c-1)*(2c+1)/(c^(2)-1). I know I must factor out (c-1) and (c^(2)-1) and the greatest common factor is (c-1). I have used algebra.com's solver and I know the answer is (2c+1)/(c+1). But how do I get (c+1) from factoring (c^(2)-1) by (c-1)? Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
c%5E2-1 Start with the given expression.


%28c%29%5E2-%281%29%5E2 Rewrite 1 as %281%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=c and B=1.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%28c%29%5E2-%281%29%5E2=%28c%2B1%29%28c-1%29 Plug in A=c and B=1.


So this shows us that c%5E2-1 factors to %28c%2B1%29%28c-1%29.


In other words c%5E2-1=%28c%2B1%29%28c-1%29.


Hopefully this helps. If not, let me know.