The numerator of a fraction is 3 less than the denominator. If 5 is added to the numerator and the denominator, the value of the resulting fraction becomes 3/4. What is the original fraction?

x = Denominator

nominator = x - 3

( x - 3 + 5 ) / ( x + 5 ) = 3 / 4

( x + 2 ) / ( x + 5 ) = 3 / 4

4 ( x + 2 ) = 3 ( x + 5 )

4 x + 8 = 3 x + 15

4 x - 3 x = 15 - 8

x = 7

Denominator = 7

The numerator is 3 less than the denominator.

Numerator = 7 - 3 = 4

original fraction = 4 /7

Proof :

( 4 + 5 ) / ( 7 + 5 ) = 9 / 12 = 3 * 3 / ( 3 * 4 ) = 3 / 4

Let's solve this step-by-step.

Step 1: Let's assume the denominator of the original fraction is represented by the variable "x".
So, the numerator of the original fraction is "x - 3".

Step 2: We are told that if 5 is added to both the numerator and the denominator, the resulting fraction is 3/4.
So, the new numerator is "x - 3 + 5" or "x + 2", and the new denominator is "x + 5".

Step 3: We can now set up an equation based on the given information:
(x + 2)/(x + 5) = 3/4

Step 4: To solve the equation, we can cross-multiply:
4(x + 2) = 3(x + 5)

Step 5: Expand the equation:
4x + 8 = 3x + 15

Step 6: Simplify the equation by subtracting 3x from both sides:
x + 8 = 15

Step 7: Subtract 8 from both sides to isolate the variable:
x = 15 - 8

Step 8: Simplify:
x = 7

Step 9: Now that we have the value of x, we can substitute it back into the original fraction to find the numerator:
Numerator = x - 3
Numerator = 7 - 3
Numerator = 4

Step 10: Therefore, the original fraction is 4/7.

To find the original fraction, let's start by setting up the equation based on the given information.

Let's assume that the denominator of the original fraction is "x". Since the numerator is 3 less than the denominator, we can represent the numerator as (x - 3).

Now, when we add 5 to both the numerator and the denominator, the resulting fraction is 3/4. So, the new numerator would be (x - 3 + 5) = (x + 2).

Forming the equation:

(x + 2) / (x + 5) = 3/4

To solve this equation and find the value of x, we can cross-multiply:

4(x + 2) = 3(x + 5)

Simplifying this equation gives us:

4x + 8 = 3x + 15

Bringing like terms to one side:

4x - 3x = 15 - 8

x = 7

Therefore, the original fraction has a numerator of (x - 3), which is (7 - 3) = 4, and a denominator of 7. Hence, the original fraction is 4/7.