Perform the addition or subtraction and simplify. (20 points)

You have to find the LCD or least common denominator.
In this case the LCD would be (x-6)(x+5).

Problem: x/ x-6 - 1/x+5

Step 1: multiply x-6 to the numerator and denominator of 1/x+5

1(x-6)/ (x+5)(x-6)

Step 2: multiply x+5 to the numerator and denominator of x/x-6
x(x+5)/ (x+5)(x-6)

After all that, this is how the problem should look now

x(x+5)/ (x-6)(x+5) - 1(x-6)/ (x-6)(x+5)

If you simplify this you get

x²+5x-x+6/ (x-6)(x+5)

If you subtract both 5x-x (like terms) you get

x²+4x+6/ (x-6)(x+5)
which is the answer