In a fraction the denominator is 5 more than numerator. when 3 is added to the numerator and 1 is added to the denominator the simplest form of the fraction is 2/3. find the original fraction.

3/8.

Step-by-step explanation:

Let the original fraction be x / (x + 5).

Then (x + 3) /  (x + 5 + 1)  = 2/3

x + 3 / x + 6 = 2 / 3

Cross multiply:

3(x + 3) = 2(x + 6)

3x + 9 = 2x + 12

x = 12 - 9 = 3

The original fraction is 3 / (3 + 5)

= 3/8.

➷ The original fraction can be written as:

x/x + 5

This is the information we have:

x + 3/x + 6 = 2/3

Cross multiply them:

3x + 9 = 2x + 12

Subtract 2x from both sides:

x + 9 = 8

Subtract 9 from both sides:

x = 3

The original fraction was 3/8

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