First we need to find the common denominator of the left side of the equation so that we can combine the terms. The second term is just 5 which can also be written as 5/1.
The common denominator is x+2, so we need to multiple both the numerator and denominator of 5/1 by x+2:
5x/(x+2) - (5*(x+2))/(1*(x+2))
5x/(x+2) - (5x+10)/(x+2)
Now subtract the numerators:
(5x - (5x + 10))/(x+2)
(5x - 5x - 10)/(x+2)
-10/(x+2)
Now we have one fraction equal to another fraction, so we can solve the proportion for x by cross multiplying.
-10/(x+2) = (x-11)/(x-2)
-10(x-2) = (x-11)(x+2)
Distribute:
-10x + 20 = x^2 + 2x - 11x - 22
Combine:
-10x + 20 = x^2 - 9x - 22
x^2 + x - 42 = 0
Factor:
(x+7)(x-6) = 0
x = -7 or x = 6