i need help with simplifying a fraction. i got as far as to factoring the denominators but I don't know what to do next. the problem is x/x^2-16+2/3x+12

Answer 1

I am going to assume you question is
x/(x^2-16) + 2/(3x+12) , those brackets are absolutely necessary to establish the correct order of operation.

It factors to
x/((x+4)(x-4)) + 2/(3(x+4))
so your LCD is 3(x+4)(x-4)
multiply top and bottom of each of the two fractions by that, then simplify.

x/((x+4)(x-4))* 3(x+4)(x-4)/(3(x+4)(x-4)) + 2/(3(x+4))*3(x+4)(x-4)/(3(x+4)(x-4))
= (3x + 2(x-4) )/(3(x+4)(x-4))
= (3x + 2x - 8)/(3(x+4)(x-4))
= (5x - 8)/(3(x+4)(x-4)) OR (5x-8)/(3(x^2 - 16))