Igot x=11 but the answer key has a different answer and i’m not real sure how to get the correct answer

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