Adding Fractions: Simplifying ((k/2k+1)+(1/(2k)(2k+2))=((k+1)/(2k+2))

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Did you forget parentheses? The correct formula is k / (2k + 1) + 1 / (2k(2k + 2)) = (k + 1) / (2k + 2)
  • #1
PhysicsBoyMan
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(k / 2k + 1) + (1 / (2k)(2k+2)) = ((k+1) / (2k+2))

I would like to simplify the left side to prove that these two statements are equal. I'm not sure how to do this. Surely I can't find a common denominator with such complex variables and such? What is a good approach?
 
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  • #2
##\frac{1}{3} + \frac{1}{8} = \frac{2}{4}## ? (##k = 1##)
 
  • #3
PhysicsBoyMan said:
(k / 2k + 1) + (1 / (2k)(2k+2)) = ((k+1) / (2k+2))

I would like to simplify the left side to prove that these two statements are equal. I'm not sure how to do this. Surely I can't find a common denominator with such complex variables and such? What is a good approach?
A good first step would be to explain what (k / 2k + 1) is supposed to mean.

Is it supposed to denote ##\frac{k}{2k + 1}## or is it supposed to denote ##\frac{k}{2k} + 1## ? The latter is what it does denote according to the PEMDAS rules.
 
  • #4
It is unclear how to interpret your fractions.
(k / 2k + 1) = k / (2k + 1)? Probably what you meant.
(k / 2k + 1) = (k / (2k)) + 1? More logical given the usual operator order (multiplication/division before addition)
(k / 2k + 1) = (k / 2)k + 1 = (k2/2) + 1? That's how a computer would interpret it.

Same thing for (1 / (2k)(2k+2)).
PhysicsBoyMan said:
Surely I can't find a common denominator with such complex variables and such?
You can always find a common denominator. Worst case: take the product of all involved denominators, that always works.
 
  • #5
Sorry, its (k / (2k + 1)) + (1 / ((2k)(2k+2))
 
  • #6
Then it is not true in general, see post #2.
 

Related to Adding Fractions: Simplifying ((k/2k+1)+(1/(2k)(2k+2))=((k+1)/(2k+2))

What is the general formula for adding fractions?

The general formula for adding fractions is (a/b) + (c/d) = (ad + bc)/bd, where a, b, c, and d are integers and b and d are not equal to 0.

Can fractions be added if they have different denominators?

Yes, fractions with different denominators can be added by finding the least common denominator (LCD) and converting each fraction to an equivalent fraction with the LCD as the denominator.

How do you simplify fractions after adding them?

To simplify fractions after adding them, you need to find the greatest common factor (GCF) of the numerator and denominator, and then divide both the numerator and denominator by the GCF.

Why is it important to simplify fractions?

Simplifying fractions helps to make them easier to work with and understand. It also helps to find equivalent fractions and compare the sizes of different fractions.

Can the formula for adding fractions be applied to algebraic fractions?

Yes, the formula for adding fractions can be applied to algebraic fractions, as long as the variables in the fractions have the same base and exponent.

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