Final answer:
To combine like terms in the equation (x)/(x+8)+5=-(8)/(x+8), we need to simplify the expression on each side of the equation. By following the steps of simplification, we find that the solution to the equation is x = -13.
Step-by-step explanation:
To combine like terms in the equation (x)/(x+8)+5=-(8)/(x+8), we need to simplify the expression on each side of the equation.
First, let's simplify the left side. Since the denominator of the first term is x+8, we can multiply both the numerator and denominator by (x+8) to get rid of the fraction. This gives us x(x+8)/(x+8) + 5(x+8)/(x+8). Simplifying further, we have x + 5(x+8)/(x+8).
Now, let's simplify the right side of the equation. To do this, we can multiply both the numerator and denominator of -(8)/(x+8) by (x+8). This gives us -8(x+8)/(x+8). Simplifying further, we obtain -8.
So, the equation becomes x + 5(x+8)/(x+8) = -8. Now we can combine like terms. Multiplying 5(x+8)/(x+8), we get 5. Therefore, the equation simplifies to x + 5 = -8. Subtracting 5 from both sides, we find that x = -13.
Therefore, the solution to the equation (x)/(x+8)+5=-(8)/(x+8) is x = -13.