x/(x^2-9) + (x+1)/(x^2+6x+9) Perform the indicated operation(s) and simplify

x/(x^2-9)+(x+1)/(x^2+6x+9)
Apply the following identities to factorize the denominators of the above rational functions:
a^2-b^2=(a+b)(a-b)  and
a^2+2ab+b^2=(a+b)^2
x/(x^2-9)+(x+1)/(x^2+6x+9)=x/(x^2-3^2)+(x+1)/(x^2+2x(3)+3^2)
=x/((x+3)(x-3))+(x+1)/(x+3)^2
LCD of the above expression is (x-3)(x+3)^2
=(x(x+3)+(x+1)(x-3))/((x-3)(x+3)^2) 
=(x^2+3x+x^2-3x+x-3)/((x-3)(x+3)^2)
Combine the like terms of the numerator,
=(x^2+x^2+3x-3x+x-3)/((x-3)(x+3)^2)
=(2x^2+x-3)/((x-3)(x+3)^2)
Factorize the numerator by splitting the middle term,
=(2x^2-2x+3x-3)/((x-3)(x+3)^2)
=(2x(x-1)+3(x-1))/((x-3)(x+3)^2)
=((2x+3)(x-1))/((x-3)(x+3)^2)
 

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