Sure, let's do this step by step:
Step 1: Make sure the denominators are the same
The denominators for both fractions are the same, i.e., (x^2 + 8x). Therefore, we can directly perform the addition of fractions.
Step 2: Perform the addition operation
Now, we add the numerator of the first fraction i.e., (x^2 - 3x) to the numerator of the second one i.e., (x^2 + 2x).
Our expression becomes:
[(x^2 - 3x) + (x^2 + 2x)] / (x^2 + 8x)
Step 3: Simplify the expression
Simplify the numerator by combining like terms:
= [2x^2 - x] / (x^2 + 8x)
Step 4: Final simplification
We can simplify our fraction further by factoring out the greatest common factor, which is x, from both numerator and denominator:
= (2x - 1) / (x + 8)
This is our final expression. Thus, (x^(2)-3x)/(x^(2)+8x) + (x^(2)+2x)/(x^(2)+8x) simplifies to (2x - 1)/(x + 8).
Remember, we assume x ≠ -8, as the denominator cannot be zero in a fraction.