SOLUTION: Please add the following rational expressions 1.{{{5n/3+4n/3}}} 2.{{{x/(x+1)(x+8)+ 8/x^2+9x+8}}} 3.{{{a/a^2-4+-2/a^2-4}}}

Algebra ->  Rational-functions -> SOLUTION: Please add the following rational expressions 1.{{{5n/3+4n/3}}} 2.{{{x/(x+1)(x+8)+ 8/x^2+9x+8}}} 3.{{{a/a^2-4+-2/a^2-4}}}      Log On


   

Question 145462: Please add the following rational expressions
1.5n%2F3%2B4n%2F3
2.x%2F%28x%2B1%29%28x%2B8%29%2B+8%2Fx%5E2%2B9x%2B8
3.a%2Fa%5E2-4%2B-2%2Fa%5E2-4
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The denominators are the same, so just add the numerators;
3 will cancel into 9:
1.%285n%29%2F3 + %284n%29%2F3 = %289n%29%2F3 = 3n
:
2.x%2F%28%28x%2B1%29%28x%2B8%29%29 + 8%2F%28%28x%5E2%2B9x%2B8%29%29
Factor the 2nd denominator and you can see that you can add the numerators:
x%2F%28%28x%2B1%29%28x%2B8%29%29 + 8%2F%28%28x%2B1%29%28x%2B8%29%29 = %28%28x%2B8%29%29%2F%28%28x%2B1%29%28x%2B8%29%29
The (x+8)'s will cancel, leaving:
1%2F%28%28x%2B1%29%29
:
Same rules apply here:
3.a%2F%28%28a%5E2-4%29%29 + %28-2%29%2F%28%28a%5E2-4%29%29 = %28%28a-2%29%29%2F%28%28a%5E2-4%29%29
However, the denominator can be factored (the difference of squares)
%28%28a-2%29%29%2F%28%28a-2%29%28a%2B2%29%29
You can see he (a-2)'s will cancel leaving us with:
1%2F%28%28a%2B2%29%29
;
:
Did this help you understand this stuff? Let me know please.