SOLUTION: (2x+4)/(x^2+2x)+3/x I know that the final answer is 5/x, but what I want to know is what happens to the 4, if to get the answer you add 2+3 to get 5.

Question 723527: (2x+4)/(x^2+2x)+3/x
I know that the final answer is 5/x, but what I want to know is what happens to the 4, if to get the answer you add 2+3 to get 5.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

We could get the denominators to match, add the fractions and then try to reduce the answer. This will work but if we can reduce the fractions we have first, it will be much easier. So let's start by trying to reduce our fractions.

When reducing fractions, only factors cancel!! So we have to factor the numerator and denominator to see if there are factors we can cancel. In the first fraction's numerator there is a common factor of 2 we can factor out. And in the first fraction's denominator there is a common factor of x we can factor out. (The second fraction does not factor so it will not reduce.) Factoring the first fraction we get:

We can now see that the factors of (x+2) will cancel:

leaving:

Not only did we make the first fraction simpler, we also made the denominators the same! So we can go ahead and them:

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