What is the difference start fraction r plus 2 over r plus 4 end fraction minus start fraction 3 over r plus 1 end fraction ?
A. start fraction negative 1 over r plus 3 end fraction
B. start fraction r superscript 2 baseline minus 1 over left parenthesis r plus 1 right parenthesis left parenthesis r plus 4 right parenthesis end fraction
C. start fraction r superscript 2 baseline minus 10 over left parenthesis r plus 1 right parenthesis left parenthesis r plus 4 right parenthesis end fraction
D. start fraction r superscript 2 baseline plus 14 over left parenthesis r plus 1 right parenthesis left parenthesis r plus 4 right parenthesis end fraction
To solve this problem, we need to simplify the given expression step by step.
The expression is: (r + 2) / (r + 4) - 3 / (r + 1)
First, let's find a common denominator for (r + 4) and (r + 1), which is (r + 1)(r + 4).
Now, we can rewrite the expression with the common denominator: [(r + 2) * (r + 1)] / [(r + 4) * (r + 1)] - [3 * (r + 4)] / [(r + 1) * (r + 4)]
Next, simplify the numerator:
(r^2 + 3r + 2) - (3r + 12)
Combining like terms, we get: r^2 + 3r + 2 - 3r - 12
Simplifying further, we have: r^2 - 10
Finally, rewrite the expression: (r^2 - 10) / [(r + 1) * (r + 4)]
So, the answer is C. start fraction r superscript 2 baseline minus 10 over left parenthesis r plus 1 right parenthesis left parenthesis r plus 4 right parenthesis end fraction.