Final answer:
The valid step in the process of solving the equation 4/2x-8+4/2x+8 = 0 is to add the like terms 4/2x and combine them, while also canceling out the -8 and +8, resulting in 4x = 0. Then divide both sides by 4, giving x = 0 as the solution.
Step-by-step explanation:
The student is trying to solve an equation and is looking for a valid step in the rearrangement of the equation 4/2x-8+4/2x+8 = 0. What we are seeking to do is combine like terms and simplify the equation in a way that allows us to isolate the variable x and solve for it.
Let's first look at the equation given: 4/2x-8+4/2x+8 = 0. The common terms 4/2x and -8+8 are apparent; we can simplify by combining them. Also, notice that the -8 and +8 will cancel each other out, because when you add a number and its opposite, you get zero. Therefore, these simplify to 0, and we are left with 4/2x + 4/2x, which simplifies to 8/2x or 4x.
After simplifying, we have the equation 4x = 0, which is the result of canceling the -8 and +8 and combining the like terms of 4/2x. The next step would be to divide both sides by 4 to isolate x, giving us x = 0. This is a practical step in the solution process.