find the sum
3x / x^2+2x+1 + 2 / x^2-4x-5

Question

find the sum 
3x / x^2+2x+1 + 2 / x^2-4x-5

anonymous · Answer

$$\frac{ 3x }{ x ^{2}+2x+1 }+\frac{ 2 }{ x ^{2}-4x-5 }$$

tkhunny · Answer

Have you considered factoring the denominators and finding a common denominator?  That's how it works with numbers, right?

anonymous · Answer

im not good with this stuff specially considering im learning from a computer

tkhunny · Answer

Nonresponsive.  Please answer my questions.

anonymous · Answer

yes and yes

tkhunny · Answer

Great.  Now actually factor the denominators, rather than just considering it.

anonymous · Answer

It can be done using partial fracions and can be made to 
$$3/(x+1) - 3/(x+1)^2 + 1/3(x+5) - 1/3(x+1)$$

tkhunny · Answer

Well, I guess we'll never know if you can factor those denominators.  riyaz has done it for you.

$x^{2}+2x+1 = (x+1)^{2}$

$x^{2}-4x-5 = (x-5)(x+1)$

Okay, now that we have the denominators factored.  Let's find the common denominator.

Note: Ignore the comment about Partial Fractions.  That also requires you to factor the denominators, but also make the addition problem we are supposed to be doing much more difficult.

anonymous · Answer

so the denominator will be (x+5)(x+1) then you add the top

tkhunny · Answer

No good.  The Least Common Denominator is $(x+1)^{2}(x-5)$.

Get both fractions to that and THEN you can add the numerators.

anonymous · Answer

thanks