How To Solve The Problem -3/P+2 = -8/P-3?

An equation means that two numbers on either side of the equals sign are equal to start with. Those two numbers are described by the two expressions. You have to  keep them equal.  You add, subtract, multiply or divide by the same number on both sides.  You do whatever you need to do to get the unknown by itself on one side.
In this case,you  might start by getting the constants on one side.
Subtract 2 so you get;
-3/P = -8/P - 5
add -8/P
5/P = -5
divide by 5
1/P = -1
multiply by P
1  = -P
multiply by -1
-1  = P
You might choose a different sequence of operations

The way it's written,

-3/P + 2 = -8/P - 3

can be solved as follows;

First, let's multiply both sides by P

-3 + 2P = -8 - 3P

add 3 to both sides;

2P = -5 - 3P

add 3P to both sides;

5P = -5

divide both sides by 5

P = -1

If you meant -3/(P+2) = -8/(P-3), then that's a completely different equation.

I'll assume you meant
-3/(p+2) = -8/(p-3)
-3(p-3) = -8(p+2)    (multiply both sides by (p+2)*(p-3))
-3p + 9 = -8p -16    (use the distributive property)
9 = -5p - 16    (add 3p to both sides)
25 = -5p    (add 16 to both sides)
25/-5 = -5 = p    (divide both sides by -5)

Check
-3/((-5)+2) = -8/((-5)-3)    (substitute -5 for p in the starting equation)
-3/-3 = -8/-8    (yes)
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If you actually meant (-3/p) + 2 = (-8/p) - 3, then that's a completely different equation.