SOLUTION: Here is my question: [w/{w^2+8w+16}] + [4/{w^2+12w+32}]. I need to add these two polynomial fractions together with variables and simplify. I've tried 2 ways already. I tried the f

Question 633134: Here is my question: [w/{w^2+8w+16}] + [4/{w^2+12w+32}]. I need to add these two polynomial fractions together with variables and simplify. I've tried 2 ways already. I tried the following 2 methods.
METHOD 1:
[w/{w^2+8w+16}] + [4/{w^2+12w+32}]
[w/(w+4)(w+4)]+[4/(w+4)(w+8)]
[w(w+8)/(w+4)(w+4)(w+8)]+[4(w+4)/(w+4)(w+8)(w+4)]
{(w^2+8w)/(w+4)(w+4)(w+8)} + [(4w+16)/(w+4)(w+4)(w+8)]
[{(w^2+12w+16)/((w+4)(w+4)(w+8)}]
But I couldn't go any further after I added the two.
METHOD 2:
Exact same but I took out one of the extra (w+4). Yet at end still had trouble.
I hope I submitted this the right way in connection with the carrot symols and the squares. And thank you in advance for your time on this problem.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Everything you did under "Method 1" is exactly correct. So

is correct.

From here there are only two things left. You should always try to reduce a fraction at the end of a problem, if possible. And after that you might want to multiply out the numerator and denominator.

To reduce the fraction, you need to have common factors in the numerator and denominator. To see if there are common factors we need the numerator and denominator factored. So it is good that you have not yet multiplied out the denominator. So we want to factor the numerator and see if there are factors to cancel. But... the numerator does not factor! So there are no common factors and this fraction will not reduce.

The only thing left, and this may or may not be required by your teacher, is to multiply out the denominator. I'll leave it up to you to decide if you are expected to multiply out the denominator and, if so, to multiply it out.
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