How to decompose the below fraction into sum of 2 terms.

In summary, the process for decomposing a fraction into a sum of 2 terms involves finding two numbers that have a common factor with the denominator of the fraction. Not all fractions can be decomposed in this way, only those with a divisible denominator. The two numbers for the denominators are chosen by finding the smallest common factor. The numerator should be distributed in a specific order, starting with the larger denominator. An example of decomposing a fraction into a sum of 2 terms is finding the common factor of the denominator, using it as the denominator for each term, and then distributing the numerator accordingly.
  • #1
JayKo
128
0
as below, my math is getting rusty, hope some can help me out.

thanks.

[tex]\frac{1}{1+\frac{1}{x}}[/tex]
 
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  • #2
First convert it into an ordinary rational expression (try simplifying

[tex]
\frac x{x\left(1 + \dfrac 1 x\right)}
[/tex]

then split the result into a sum of two pieces.

Alternately, notice that [itex] 1 = 1 + \frac 1 x - \frac 1 x [/itex] and use that in the numerator.
 

Related to How to decompose the below fraction into sum of 2 terms.

1. What is the process for decomposing a fraction into a sum of 2 terms?

The process for decomposing a fraction into a sum of 2 terms involves finding two numbers that have a common factor with the denominator of the fraction. These two numbers will then be used as the denominators for the two terms, while the numerator of the fraction is distributed between the two terms.

2. Can any fraction be decomposed into a sum of 2 terms?

No, not all fractions can be decomposed into a sum of 2 terms. Only fractions that have a denominator that is divisible by a common factor can be decomposed in this way.

3. How do you choose the two numbers for the denominators when decomposing a fraction?

The two numbers for the denominators are chosen by finding a common factor with the denominator of the fraction. This common factor should be as small as possible in order to simplify the fraction.

4. Is there a specific order in which the numerator should be distributed between the two terms?

Yes, when decomposing a fraction into a sum of 2 terms, the numerator should be distributed in a specific order. The larger of the two denominators should be used first, and then the remaining numerator should be distributed to the other term.

5. Can you provide an example of decomposing a fraction into a sum of 2 terms?

For example, let's decompose the fraction 5/15 into a sum of 2 terms. The common factor of 15 is 5, so we will use 5 and 3 as the denominators. The numerator of 5/15 is 5, so we will distribute 5 to the first term, making it 5/5. The remaining numerator of 0 will go to the second term, making it 0/3. Therefore, 5/15 can be decomposed into 5/5 + 0/3, which simplifies to 1 + 0, or simply 1.

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