SOLUTION: m^2+7m+12/m^2-8m+16 + m+3/m^2-16 =(m+3)(m+4)/(m-4)(m-4)+(m+3)/(m-4)(m-4) =(m+3)(m+4)(m+4)/(m-4)(m-4)(m+4)+(m+3)(m-4)/(m-4)(m-4)(m+4) =(m+3)((m+4)(m+4)+(m-4)/((m-4)(m-4)(m+4) =(

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: m^2+7m+12/m^2-8m+16 + m+3/m^2-16 =(m+3)(m+4)/(m-4)(m-4)+(m+3)/(m-4)(m-4) =(m+3)(m+4)(m+4)/(m-4)(m-4)(m+4)+(m+3)(m-4)/(m-4)(m-4)(m+4) =(m+3)((m+4)(m+4)+(m-4)/((m-4)(m-4)(m+4) =(      Log On


   

Question 261313: m^2+7m+12/m^2-8m+16 + m+3/m^2-16
=(m+3)(m+4)/(m-4)(m-4)+(m+3)/(m-4)(m-4)
=(m+3)(m+4)(m+4)/(m-4)(m-4)(m+4)+(m+3)(m-4)/(m-4)(m-4)(m+4)
=(m+3)((m+4)(m+4)+(m-4)/((m-4)(m-4)(m+4)
=(m+3)(m^2+8m+16+m-4)/((m-4)(m-4)(m+4)
=(m+3)(m^2+9m+12)/(m-4)(m-4)(m+4)
OR
m^2+7m+12/m^2-8m+16 + m+3/m^2-16
=(m+3)(m+4)/(m-4)(m-4)+(m+3)/(m-4)(m-4)
=(m+3)(m+4)(m+4)+(m+3)(m-4)/(m-4)(m-4)(m+4)
=(m^2+7m+12)(m+4)+(m^2-m-12)/(m-4)(m-4)(m+4)
=(m^3+7m^2+12m+4m^2+28m+48)+(m^2-m-12)/(m-4)(m-4)(m+4)
=(m^3+11m^2+40m+48+m^2-m-12)/(m-4)(m-4)(m+4)
=(m^3+12m^2+39m+36)/(m-4)(m-4)(m+4)
= m(m^2+12m+39)+36/(m-4)(m-4)(m+4)
Are any of these correct? If yes, which one is? If not, please show me how to do this correctly. Thank you very much!
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

These are both correct, except you had a %28m-4%29 
where I placed the red red%28%28m%2B4%29%29, but I think that 
was just a typo, since the rest is correct, and you solved 
it as though you hadn't made that error. However, there should be
one more step at the end:

%28m%5E2%2B7m%2B12%29%2F%28m%5E2-8m%2B16%29+%2B+%28m%2B3%29%2F%28m%5E2-16%29



%22%22=%28%28m%2B3%29%28m%5E2%2B8m%2B16%2Bm-4%29%29%2F%28%28m-4%29%28m-4%29%28m%2B4%29%29
%22%22=%28%28m%2B3%29%28m%5E2%2B9m%2B12%29%29%2F%28%28m-4%29%28m-4%29%28m%2B4%29%29 

Now you should write %28m-4%29%28m-4%29 as %28m-4%29%5E2:

%22%22=%28%28m%2B3%29%28m%5E2%2B9m%2B12%29%29%2F%28%28m-4%29%5E2%28m%2B4%29%29

Your second one has that same error in the first step, 
but the rest is right, you just multiplied out the top, 
wheareas you didn't the first way.  Both answers are
equivalent:

%28m%5E2%2B7m%2B12%29%2F%28m%5E2-8m%2B16%29+%2B+%28m%2B3%29%2F%28m%5E2-16%29


%22%22=%28m%5E3%2B11m%5E2%2B40m%2B48%2Bm%5E2-m-12%29%2F%28%28m-4%29%28m-4%29%28m%2B4%29%29
%22%22=%28m%5E3%2B12m%5E2%2B39m%2B36%29%2F%28%28m-4%29%28m-4%29%28m%2B4%29%29
%22%22=cross%28%28m%28m%5E2%2B12m%2B39%29%2B36%29%2F%28%28m-4%29%28m-4%29%28m%2B4%29%29%29

Now there was no point in factoring m out of just the first three
terms of that numerator.  It wasn't wrong but it led nowhere. That's 
why I crosed it out. Your last step should have been just to write
the %28m-4%29%28m-4%29 as %28m-4%29%5E2, and leave the answer as

%22%22=%28m%5E3%2B12m%5E2%2B39m%2B36%29%2F%28%28m-4%29%5E2%28m%2B4%29%29 

Both your answers are correct.  Good job!

Edwin