simplify r^2/((r+4)(sqrt(r^2+9)+3))
To simplify the expression r^2/((r+4)(sqrt(r^2+9)+3)), we can start by factoring r^2+9 as a difference of squares:
r^2+9 = (r^2+3^2) = (r+3)(r-3)
Now we can rewrite the expression as:
r^2/((r+4)(sqrt(r^2+9)+3)) = r^2/((r+4)(sqrt((r+3)(r-3))+3))
Next, we can simplify the denominator by multiplying out the square root term:
(sqrt((r+3)(r-3))+3) = sqrt(r+3)*sqrt(r-3) + 3
Substituting this back into the expression, we have:
r^2/((r+4)(sqrt(r^2+9)+3)) = r^2/((r+4)(sqrt(r+3)*sqrt(r-3) + 3))
Since we cannot simplify this expression further, this is the simplified form of the given expression.
To simplify the expression r^2/((r+4)(sqrt(r^2+9)+3)), you can start by simplifying the denominator.
Let's begin by simplifying the term sqrt(r^2+9) + 3. We can combine the terms inside the square root:
sqrt(r^2+9) + 3 can be rewritten as sqrt(r^2+9) + 3 * sqrt(1) because sqrt(1) is equal to 1.
Therefore, sqrt(r^2+9) + 3 can be simplified to sqrt(r^2+9) + 3 * 1.
Next, we simplify the denominator by multiplying (r+4) with sqrt(r^2+9) + 3 * 1:
(r+4) * (sqrt(r^2+9) + 3 * 1) can be further simplified as (r+4) * (sqrt(r^2+9) + 3) because 3 * 1 is equal to 3.
Now we can rewrite the initial expression r^2/((r+4)(sqrt(r^2+9)+3)) as r^2/(r+4) * 1/(sqrt(r^2+9) + 3).
Finally, you cannot simplify this expression any further since there are no common factors or terms to cancel out. Hence, the simplified form of r^2/((r+4)(sqrt(r^2+9)+3)) is r^2/(r+4) * 1/(sqrt(r^2+9) + 3).
To simplify the expression r^2/((r+4)(sqrt(r^2+9)+3)), we can start by simplifying the denominator.
First, let's expand the denominator (r+4)(sqrt(r^2+9)+3):
(r + 4) * sqrt(r^2 + 9) + (r + 4) * 3
Next, we can distribute the terms:
r * sqrt(r^2 + 9) + 4 * sqrt(r^2 + 9) + 3r + 12
Now, we can simplify the expression by combining like terms:
(r * sqrt(r^2 + 9) + 3r) + (4 * sqrt(r^2 + 9) + 12)
Finally, let's factor out r from the first two terms and factor out 4 from the last two terms:
r * (sqrt(r^2 + 9) + 3) + 4 * (sqrt(r^2 + 9) + 3)
Now, the denominator becomes:
(r * (sqrt(r^2 + 9) + 3) + 4 * (sqrt(r^2 + 9) + 3))
We can now substitute the simplified denominator back into the original expression, r^2/((r+4)(sqrt(r^2+9)+3)):
r^2/((r * (sqrt(r^2 + 9) + 3) + 4 * (sqrt(r^2 + 9) + 3)))
We can further simplify the expression by canceling out common factors in the numerator and denominator, if any. However, if any further simplification is possible, it would depend on the specific value or range of values for r.