Solve the following inequality.

(x-4/-x+2)>0

Write your answer using interval notation.

You need parentheses.

x - (4/-x) + 2 > 0 ?
(x - 4)/(-x + 2) > 0 ?

Please, re-state the problem with parentheses.

To solve the inequality (x-4)/(-x+2)>0, we need to find the values of x that make the expression greater than zero.

To do this, we first need to find the values of x that make the expression equal to zero. This occurs when the numerator, (x-4), equals zero. So, setting (x-4) = 0 and solving for x, we find x = 4.

Next, we need to find the values of x that make the denominator, (-x+2), equal to zero. Setting (-x+2) = 0 and solving for x, we find x = 2.

Now, we have three critical points: x = 4, x = 2 from setting the numerator and denominator to zero, and -∞ from the negative sign in the denominator.

To determine the intervals where the expression is greater than zero, we can use a number line.

Let's test the intervals one by one:

1. For x < 2:
- If we choose x = 0 (a value less than 2), the expression becomes (-4 / -2) = 2, which is positive. So, this interval satisfies the inequality.

2. For 2 < x < 4:
- If we choose x = 3 (a value between 2 and 4), the expression becomes (-1 / -1) = 1, which is not greater than zero. So, this interval does not satisfy the inequality.

3. For x > 4:
- If we choose x = 5 (a value greater than 4), the expression becomes (1 / -3) = -1/3, which is negative. So, this interval does not satisfy the inequality.

Therefore, the solution to the inequality (x-4)/(-x+2) > 0 is x < 2 or x > 4.

In interval notation, the solution can be written as (-∞, 2) ∪ (4, +∞).