Fraction Decomposition: A/a+B/b?

In summary, fraction decomposition is the process of breaking down a single fraction into simpler fractions with different denominators. It is useful in solving complex algebraic equations and simplifying expressions. To decompose fractions, one needs to find the common denominator, multiply the numerators by the opposite denominator, and simplify the resulting fractions. All fractions can be decomposed, but some may already be in their simplest form. Real-world applications of fraction decomposition include solving problems in engineering, chemistry, economics, cooking, and baking.
  • #1
priced02
4
0
Just wondering - is there anything you can do with 1/(a + b) to get something like A/a + B/b?
 
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  • #2
character string manipulations
 
  • #3
yes, but your B's and A's may be in terms of a and b or even 0. Making it kind of useless...
 
  • #4
lalbatros said:
character string manipulations

lol... by the way, I don't think the original question is possible in general. of course, as JonF mentioned... you can have:

[tex]a\cdot\frac{\frac{1}{a+b}}{2a}+b\cdot\frac{\frac{1}{a+b}}{2b}[/tex]

which is utterly useless.
 

Related to Fraction Decomposition: A/a+B/b?

1. What is fraction decomposition?

Fraction decomposition is the process of breaking down a single fraction into two or more simpler fractions with different denominators.

2. Why is fraction decomposition useful?

Fraction decomposition can be useful in solving complex algebraic equations involving fractions, as well as in simplifying expressions and finding common denominators.

3. How do you decompose fractions?

To decompose fractions, you need to first find the common denominator of the two fractions. Then, multiply the numerators of each fraction by the opposite denominator and combine the fractions. Finally, simplify the resulting fractions, if necessary.

4. Can all fractions be decomposed?

Yes, all fractions can be decomposed into simpler fractions. However, some fractions may already be in their simplest form and do not require decomposition.

5. What are some real-world applications of fraction decomposition?

Fraction decomposition is used in various fields such as engineering, chemistry, and economics to solve problems involving proportions and ratios. It is also used in everyday tasks such as cooking and baking, where precise measurements are needed.

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