SOLUTION: Please help with these two questions. I dont understand and I have tried to do the work but it's to confusing. PLEASE HELP ME!!!!!! 1) x^2 + 9 ___ __ x+3 x+3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help with these two questions. I dont understand and I have tried to do the work but it's to confusing. PLEASE HELP ME!!!!!! 1) x^2 + 9 ___ __ x+3 x+3       Log On


   

Question 116841: Please help with these two questions. I dont understand and I have tried to do the work but it's to confusing. PLEASE HELP ME!!!!!!
1) x^2 + 9
___ __
x+3 x+3

2) x^2+2x - x^2+5x+6
_____ _______
3x 3x
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I think what you are trying to write is: %28x%5E2%2F%28x%2B3%29%29%2B9%2F%28x%2B3%29 and %28%28x%5E2%2B2x%29%2F3x%29-%28%28x%5E2%2B5x%2B6%29%2F3x%29

You don't tell us in your problem statement, but I'm going to assume that you are trying to add the fractions and then simplify.

Start by remembering back when you first started adding fractions. If the denominators of two fractions you are trying to add are equal, then you simply add the numerators. Symbolically, the rule looks like this: %28a%2Fc%29%2B%28b%2Fc%29=%28a%2Bb%29%2Fc

In both of your problems, the denominators are identical, so all you need do is add the numerators.

%28x%5E2%2F%28x%2B3%29%29%2B9%2F%28x%2B3%29=%28x%5E2%2B9%29%2F%28x%2B3%29. There is no real number factorization of x%5E2%2B9, or to put it another way, x%2B3 is not a factor of x%5E2%2B9 so there is no more that you can do with this.


Now apply the same rule to the second problem:
%28%28x%5E2%2B2x%29%2F3x%29-%28%28x%5E2%2B5x%2B6%29%2F3x%29=%28x%5E2%2B2x-x%5E2-5x-6%29%2F3x, then collect like terms:

%280x%5E2-3x-6%29%2F3x=%28-3x-6%29%2F3x, and then factor out the 3 from the numerator
3%28-x-2%29%2F3x=%28-x-2%29%2Fx, and that is as simple as this one gets.

Hope this helps,
John