Homework Help: How do I simplify this fraction?

1. Sep 14, 2011

polishdude20

1. The problem statement, all variables and given/known data

Simplify the following expression by rewriting it as a single simple fraction in simplest form:

2. Relevant equations

not much just factoring and solving for P

3. The attempt at a solution

I tried to factor the fractions by multiplying the denominators with the numerators and after much writing on paper I came up with : (p+5)/(p^2-16) , I also came up with : (fp^2+p)/(p^3-16p)

I'm stumped here as to how much I have to factor or simplify or even even I did it right?

2. Sep 14, 2011

dangish

You are right in the sense that you need a common denominator..

Would this help?

5/(p+4) - 5/p(p-2) + 4/(p-4)(p+4)

3. Sep 14, 2011

polishdude20

it's supposed to be "5/p(p-4)" but I've done it with ALOT of writing, this stuff fills up your page fast doesn't it?

4. Sep 14, 2011

dangish

Well if you got it, who cares? Haha

5. Sep 14, 2011

Dick

It can. But 5/(p(p-4)) isn't right. Putting p=1 in your original expression I get 12/5. Putting p=1 into 5/(p(p-4)) gives -5/3. That isn't right. Is there a typo?

6. Sep 14, 2011

polishdude20

I don't know dick but I got the answer figured out after doing some more thinking, if you guys want to see a solution just wolfram alpha it.. I didn't do it that way though..

7. Sep 15, 2011

Mentallic

Well I hope you didn't get 5/(p(p-4)) as the answer, because it's not right!

8. Sep 15, 2011

symbolipoint

Lowest Common Denominator is $p(p+4)(p-4)$.

Multiply each rational term by 1 using the suitable factors from the LCD,
$\frac{5}{(p+4)}\frac{p(p-4)}{p(p-4)}-\frac{5}{p(p-4)}\frac{p+4}{p+4}+\frac{4}{(p+4)(p-4)}\frac{p}{p}$

Perform the needed multiplications for the numerator and look for any further simplifications.

9. Sep 15, 2011

polishdude20

nono! I said that because somone else wrote the wrong thing and stuff.