How do I simplify this fraction?

In summary, the student attempted to solve for homework equations by factoring and simplifying. However, they were not able to get the answer correct and needed help from their teacher.
  • #1
polishdude20
9
0

Homework Statement

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

Homework Equations



not much just factoring and solving for P

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?
 
Physics news on Phys.org
  • #2
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
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
Well if you got it, who cares? Haha
 
  • #5
polishdude20 said:
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?

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
Dick said:
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?

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
polishdude20 said:
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..

Well I hope you didn't get 5/(p(p-4)) as the answer, because it's not right!
 
  • #8
Lowest Common Denominator is [itex] p(p+4)(p-4)[/itex].

Multiply each rational term by 1 using the suitable factors from the LCD,
[itex]\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}[/itex]

Perform the needed multiplications for the numerator and look for any further simplifications.
 
  • #9
Mentallic said:
Well I hope you didn't get 5/(p(p-4)) as the answer, because it's not right!

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

What does it mean to simplify a fraction?

Simplifying a fraction means reducing it to its simplest form by dividing the numerator and denominator by their greatest common factor. This results in a fraction that has the smallest possible numerator and denominator.

How do I find the greatest common factor?

The greatest common factor (GCF) is the largest number that can evenly divide both the numerator and denominator of a fraction. To find the GCF, you can list out the factors of each number and find the largest one that they have in common, or you can use the prime factorization method.

Can I simplify a fraction with variables?

Yes, you can simplify a fraction with variables by following the same steps as simplifying a fraction with numbers. You can also use algebraic techniques, such as factoring, to simplify fractions with variables.

What if the fraction has a negative sign?

If the fraction has a negative sign, you can simplify it by moving the negative sign to either the numerator or denominator. This will not change the value of the fraction, and you can then proceed with simplifying it as usual.

Is there a shortcut for simplifying fractions?

Yes, there are some shortcuts for simplifying fractions, such as using the "cross-multiplication" method or using the "canceling" method. However, it is important to understand the concept of simplifying fractions and the steps involved in order to use these shortcuts correctly.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
16
Views
2K
  • Precalculus Mathematics Homework Help
Replies
5
Views
2K
  • Precalculus Mathematics Homework Help
Replies
14
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
3K
  • Precalculus Mathematics Homework Help
Replies
2
Views
3K
  • Precalculus Mathematics Homework Help
Replies
4
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
3K
  • Precalculus Mathematics Homework Help
Replies
11
Views
3K
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
Back
Top