Simplify the sum. Must show work

Question

4/(x+3)+8/x(x+3)

Answer 1

To simplify the sum, we need to find a common denominator for both terms. The common denominator in this case is x(x+3).

4/(x+3) + 8/x(x+3)

The first term already has the common denominator, so we don't need to change anything.

Now we need to convert the second term to have the same denominator as the first term:

8/x(x+3) can be written as 8x/(x*x+3x) = 8x/(x^2+3x) = 8x/(x^2+3x)

Now the sum becomes:

4/(x+3) + 8x/(x^2+3x)

Now that both terms have the same denominator, we can combine them:

(4+8x)/(x^2+3x)

Therefore, the simplified sum is (4+8x)/(x^2+3x).