# Thread: Adding rational expr: 5 / (x^3 - y^3) + 3 / (x^2 + xy + y^2)

1. ## Adding rational expr: 5 / (x^3 - y^3) + 3 / (x^2 + xy + y^2)

The problem: 5 / (x^3 - y^3) + 3 / (x^2 + xy + y^2) = ?

My work so far: 5 / (x - y(x^2 - y^2)) + 3 / [(x + y)(x + y)]

I don't know what to do from here for a common denominator

thank you
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Edited by stapel -- Reason for edit: attempting to restore formatting and thus meaning

2. Is this your problem?. Try using LaTex. Your post got all mixed up. Hard to read.

$\L\\\frac{5}{x^{3}-y^{3}}+\frac{3}{x^{2}+xy+y^{2}}$

If this is correct, you should recognize the difference of two cubes.

$\L\\x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$

3. ## Re: Adding rational expressions

Originally Posted by alee
Code:
5                  +                    3
-------------               ------------------   =
x^3 - y^3      +         x^2 + xy + y^2

Are these two separate problems?

Code:
    5                    +              3
---------------          ---------------   =
x-y(x^2-y^2)    +     (x+y)(x+y)

4. ## Re: Adding rational expressions

Originally Posted by alee
5 + 3
------------- ------------------ =
x^3 - y^3 + x^2 + xy + y^2

5 + 3
--------------- --------------- =
x-y(x^2-y^2) + (x+y)(x+y)

I don't know what to do from here for a common denominator

thank you
first, note that $\L x^2 + xy + y^2 \neq (x+y)(x+y)$.
second, note galactus' factorization of $\L x^3 - y^3$. the common denominator will be $\L x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ ...

$\L \frac{5}{(x-y)(x^2 + xy + y^2)} + \frac{3(x-y)}{(x-y)(x^2 + xy + y^2)}$ ... add'em up.

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