Express as a single fraction n/(n-3) - n/(n+2)

  • Thread starter Gringo123
  • Start date
  • Tags
    Fraction
In summary, the conversation is about solving the equation n/(n-3) - n/(n+2) and the correct answer is 5/4. The method used was to assign a value to n and simplify the equation using the LCM of the denominators. It was confirmed by another person that the answer was correct and the solution was valid for other values of n as well.
  • #1
Gringo123
141
0
n/(n-3) - n/(n+2)

I have tried to solve this by giving n a value. I chose n = 6, which gives:

6/3 - 6/8

The LCM of 3 and 8 is 24 so...

6/3 - 6/8 = 48/24 - 18/24 which gives 30/24

Final answer = 5/4

Is that the correct answer and have I used the correct method of solving the problem?
 
Physics news on Phys.org
  • #2
Hi Gringo123! :smile:
Gringo123 said:
n/(n-3) - n/(n+2)

I have tried to solve this by giving n a value. I chose n = 6, which …

Sorry, but that's madness. :redface:

The question is asking for p(n)/q(n), where p and q are both polynomials in n.

(For example, 1/(n-1) + 1/(n+1) = 2n/(n2-1). :wink:)
 
  • #3
Yes for n=6 your solution is correct. But n can take few more values to get a fraction.
 
  • #4
I think I have it now
ans = 5n / (n-3)(n+2)
 
  • #5
Yup! :biggrin:
 

Related to Express as a single fraction n/(n-3) - n/(n+2)

1. What is the simplified form of the expression n/(n-3) - n/(n+2)?

The expression can be simplified by finding the least common denominator (LCD) of (n-3) and (n+2), which is (n-3)(n+2). Multiplying the first fraction by (n+2) and the second fraction by (n-3) gives us n(n+2)/(n-3)(n+2) - n(n-3)/(n-3)(n+2). Combining like terms gives us n(n+2 - n(n-3))/(n-3)(n+2), which simplifies to 6/(n-3)(n+2).

2. Can the expression n/(n-3) - n/(n+2) be further simplified?

No, the expression is already in its simplest form. The LCD (n-3)(n+2) cannot be factored further, and the fractions cannot be combined any further.

3. Is it possible for the expression to be undefined?

Yes, the expression is undefined when the denominator (n-3) or (n+2) is equal to 0. In these cases, the fraction would be dividing by 0, which is undefined in mathematics.

4. How can this expression be applied in real-life situations?

This expression can be used in situations where there are two fractions representing the same quantity, but with different denominators. For example, if a recipe calls for 1/3 cup of flour and another recipe calls for 1/4 cup of flour, we can combine these fractions to get a total amount of flour needed.

5. Can this expression be solved for a specific value of n?

Yes, the expression can be solved for a specific value of n by plugging in the value for n and evaluating the resulting expression. For example, if n=5, the expression becomes 5/(5-3) - 5/(5+2), which simplifies to 1/2 - 5/7. This can be further simplified to -9/14.

Similar threads

Find the values of ## n\geq 1 ## for which ## 1+2+3+\dotsb +n ##.
    • Precalculus Mathematics Homework Help
Replies
4
Views
829
Express ##x^3+y^3## in terms of ##m## and ##n##
    • Precalculus Mathematics Homework Help
Replies
17
Views
346
In the expansion of ##(1+x)^n##, the coefficients of terms equidistant from the beginning and the end are equal
    • Precalculus Mathematics Homework Help
Replies
3
Views
717
Prove that ## p_{n+3}^{2}<p_{n} p_{n+1} p_{n+2} ##
    • Precalculus Mathematics Homework Help
Replies
10
Views
969
Probability of getting the smallest value of cards
    • Precalculus Mathematics Homework Help
Replies
9
Views
1K
Find the nth term of the given sequence
    • Precalculus Mathematics Homework Help
Replies
7
Views
1K
Why Does Flipping the Denominator in Complex Fractions Give the Wrong Answer?
    • Precalculus Mathematics Homework Help
Replies
9
Views
670
Verify that ## L(1, \chi)\neq 0 ##
    • Precalculus Mathematics Homework Help
Replies
4
Views
837
Number of ways of arranging 7 characters in 7 spaces
    • Precalculus Mathematics Homework Help
Replies
8
Views
600
How to find z^n of a complex number
    • Precalculus Mathematics Homework Help
Replies
12
Views
1K

Hot Threads

Recent Insights

Back
Top