posted by Stacey on .
Simplify each rational expression. Can you please show me the steps on how you got the answer. Thank you
(over means there is a line under the first expression and then the second expression is placed underneath the line)
2c^2-c-1 over 2c^2+3c+1
8c^2+2c over 4c+1
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!