Posted by Stacey on Sunday, April 25, 2010 at 6:31pm.
Stacey,
Given any rational expression, your first instinct should be to factor the numerator (if possible), then factor the denominator (if possible), then divide out and common factors. So, assuming you know how to factor . . .
2c^2-c-1 --> (2c+1)(c-1)
2c^2+3c+1 --> (2c+1)(c+1)
Once factoring is completed, you will notice that there is a common binomial on top and bottom, namely (2c+1). That can be canceled out, leaving a final answer of (c-1)/(c+1).
WARNING: DO NOT CANCEL OUT THE C's. You can cancel factors but NOT TERMS.
For the 2nd example:
8c^2+2c --> 2c(4c+1)
4c+1 -----> 4c+1
The common binomial of (4c+1) cancels out, thus leaving you with 2c as you final answer.
Hope this helps!
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