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
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!
To simplify rational expressions, we need to factor the numerator and the denominator (if possible), and then cancel out any common factors that appear in both the numerator and the denominator.
Let's start with the first rational expression:
(2c^2 - c - 1) / (2c^2 + 3c + 1)
1. Factor both the numerator and the denominator:
The numerator can be factored as (2c + 1)(c - 1).
The denominator can be factored as (2c + 1)(c + 1).
2. Cancel out any common factors:
In this case, we can cancel out the (2c + 1) factor present in both the numerator and the denominator.
Simplifying the first rational expression, we get:
(2c + 1)(c - 1) / (c + 1)
Now let's move on to the second rational expression:
(8c^2 + 2c) / (4c + 1)
1. Factor out the common factors:
In this case, both the numerator and the denominator have a common factor of 2c.
So, we can factor it out: 2c(4c + 1) / (4c + 1)
2. Cancel out the common factor:
Since we have cancelled out the (4c + 1) factor from both the numerator and the denominator, the final simplified form is:
2c