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If 3 is subtracted from the numerator of a certain fraction, the value of the fraction becomes 3/5. If 1 is subtracted from the denominator of the same fraction, it becomes 2/3. Find the original fraction.

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Let the certain fraction = x/y

If 3 is subtracted from the numerator, the value is 3/5.

(x-3)/y = 3/5

5(x-3) = 3y

5x - 15 = 3y

5x - 3y = 15 [1]

If 1 is subtracted from tbe denominator of the same fraction, it becomes 2/3.

x/(y-1) = 2/3

3x = 2(y-1)

3x = 2y - 2

3x = 2y - 2

3x - 2y = -2 [2]

Multiply [1] by 2 and [2] by 3:

10x - 6y = 30

9x - 6y = -6

Subtracting eliminates y; find x , 1x = 36 is the numerator:

Find y using: 5x - 3y =15

5(36) - 3y = 15

y = 55 is the denominator

**x/y = 36/55 ***(certain fraction)*

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