Find lowest common denominator of these polynomials

In summary, the conversation is about finding the lowest common denominator for the expression 3/x^2+2x - 2/x^2+x-2 + 4/x^2(x-1) and how to simplify it. The expert guides the student to factor the expression and determine the LCD to be x^2(x-1)(x+2).
  • #1
Makman
10
0

Homework Statement


3/x^2+2x - 2/x^2+x-2 + 4/x^2(x-1)
Find the lowest common denominator and solve.


Homework Equations





The Attempt at a Solution



I factored x(x+2) - (x-1)(x+2) + x^2(x-1)

It looks like (x+2), (x-1) are common but what to do with the x & x^2 left over?
Thank you in advance.
 
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  • #2
Hi Makman! :smile:
Makman said:
3/x^2+2x - 2/x^2+x-2 + 4/x^2(x-1)
Find the lowest common denominator and solve.
…
I factored x(x+2) - (x-1)(x+2) + x^2(x-1)

It looks like (x+2), (x-1) are common …

Nooo … you're looking at this the wrong way …

Hint: the LCD of, say, 1/2*3 and 1/3*5 would be 2*3*5 :wink:
 
  • #3


If I take your example and it was 1/6 + 1/15 my answer would be 7/30. 30 being the common denominator. As I understand it, 90 could be a common denominator but it is not the lowest.
What should I do with the denominator in the original problem to make things more clear. I'm not cluing in. My apologies.
Please help.
Thank you.
 
  • #4
Makman said:
If I take your example and it was 1/6 + 1/15 my answer would be 7/30. 30 being the common denominator. As I understand it, 90 could be a common denominator but it is not the lowest.
What should I do with the denominator in the original problem to make things more clear. I'm not cluing in. My apologies.
Please help.
Thank you.

ok … when you had 2*3 and 3*5, you needed to include everything the minimum number of times… that's 2*3*5.

so when you have x(x+2) (x-1)(x+2) and x2(x-1), again you could just multiply everything, to give x(x+2)(x-1)(x+2)x2(x-1), but you can cut that down to … ? :smile:
 
  • #5


I believe I got it. The L.C.D. would be x^2(x-1)(x+2). Is this correct?
 
  • #6
:biggrin: Woohoo! :biggrin:​
 
  • #7


Thank you for your time and patience.:approve:
 

FAQ: Find lowest common denominator of these polynomials

What is the definition of a lowest common denominator (LCD) for polynomials?

The lowest common denominator (LCD) for polynomials is the smallest polynomial that is a multiple of all the denominators in the given set of fractions. It is used to simplify complex fractions and make them easier to work with.

How do you find the lowest common denominator for two polynomials?

To find the lowest common denominator for two polynomials, first factor each polynomial into its prime factors. Then, identify the common prime factors between the two polynomials and multiply them together. Finally, multiply any remaining unique prime factors to the LCD.

Can there be more than one lowest common denominator for a set of polynomials?

No, there can only be one lowest common denominator for a set of polynomials. This is because the LCD is the smallest polynomial that can be used to simplify all the fractions in the set.

What if the polynomials have variables with different exponents?

If the polynomials have variables with different exponents, you can still find the lowest common denominator by factoring each polynomial and then identifying the common factors. The common factors will include all the variables with the highest exponent for each variable.

How is finding the lowest common denominator of polynomials useful in math?

Finding the lowest common denominator of polynomials is useful in math because it allows us to simplify complex fractions and make them easier to work with. It is also helpful when adding or subtracting fractions with different denominators, as it allows us to find a common denominator that can be used for all the fractions.

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