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Please explain how to do this
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Please explain how to do this Show working-example-1
User Chihiro
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2 Answers

4 votes

Answer:

a = 3b/b-3

because combined the expression and leaving alone the variable

User Rickumali
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8.8k points
12 votes

Answer:

(A, B) = (4, 12) or (12, 4)

Explanation:

An Egyptian fraction is the sum of distinct unit fractions. Here, we're asked to decompose 1/3 into an Egyptian fraction sum of two fractions. There are formulas available when the sum has a numerator value of 2.

Here, the sum is a unit fraction. A reasonable approach is to use 1/(n+1) as the larger portion of 1/n. Then the other portion is 1/(n(n+1)). That is effectively what we end up with here.

__

Multiplying by 3AB gives ...

AB = 3B +3A

Solving for B, we find ...

AB -3B = 3A

B(A -3) = 3A

B = 3A/(A -3)

In order for A-3 to be a factor of A, or equal to 3, we must have ...

A-3 = 1 ⇒ A = 4

A-3 = 3 ⇒ A = 6

A-3 = 3×3 ⇒ A = 4×3

This will give integer values for B when A is one of 4, 6, or 12. In the case of A=6, the two fractions are equal, which is not what you want

The two solutions are ...

(A, B) = (4, 12) or (12, 4)

User Milen Dyankov
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