a) To solve 5/(x-3) = 0, we need to find the value of x that makes the equation true.

Since division by zero is undefined, the denominator (x-3) cannot be equal to zero. Therefore, x ≠ 3.

There is no solution to this equation.

b) To solve 5/(x-3) > 0, we need to find the values of x that make the inequality true.

First, let's find the critical points by setting the numerator and denominator equal to zero:

Numerator: 5 = 0 (No solution)
Denominator: x - 3 = 0
x = 3

Now, we can create a number line and test different intervals:

Test x < 3: Choose x = 2
5/(2-3) = 5/(-1) = -5 < 0 (Not true)

Test x > 3: Choose x = 4
5/(4-3) = 5/1 = 5 > 0 (True)

Therefore, the solution to 5/(x-3) > 0 is x > 3.

c) There is no equation or inequality provided.

d) To solve 5/(x-3) = 0, we need to find the value of x that makes the equation true.

Since division by zero is undefined, the denominator (x-3) cannot be equal to zero. Therefore, x ≠ 3.

There is no solution to this equation.

e) To solve 5/(x-3) > 0, we need to find the values of x that make the inequality true.

First, let's find the critical points by setting the numerator and denominator equal to zero:

Numerator: 5 = 0 (No solution)
Denominator: x - 3 = 0
x = 3

Now, we can create a number line and test different intervals:

Test x < 3: Choose x = 2
5/(2-3) = 5/(-1) = -5 < 0 (Not true)

Test x > 3: Choose x = 4
5/(4-3) = 5/1 = 5 > 0 (True)

Therefore, the solution to 5/(x-3) > 0 is x > 3.

f) There is no equation or inequality provided.

g) To solve -5/(x-3) > 0, we need to find the values of x that make the inequality true.

First, let's find the critical points by setting the numerator and denominator equal to zero:

Numerator: -5 = 0 (No solution)
Denominator: x - 3 = 0
x = 3

Now, we can create a number line and test different intervals:

Test x < 3: Choose x = 2
-5/(2-3) = -5/(-1) = 5 > 0 (True)

Test x > 3: Choose x = 4
-5/(4-3) = -5/1 = -5 < 0 (Not true)

Therefore, the solution to -5/(x-3) > 0 is x < 3.

Note: It seems like there was a mistake in the original question as options c), f), and k) were not provided.