Let the fraction be x/y. We're given two equations:

- x/y = 3/4
- (x + 7)/y = 4/3.
*(The reciprocal of 3/4 is found by 1/(3/4)*

- 4x = 3y
- 3(x + 7) = 4y

- 4x = 3y
- 3x + 21 = 4y

- x = 3y/4
- 3x + 21 = 4y

3(3y/4) + 21 = 4y

9y/4 + 21 = 4y

Multiply the equation by 4 on both sides to eliminate the denominator:

9y + 84 = 16y

To solve this equation for y, we type it in our math engine and we get:

y =

**12**

We then substitute y = 12 into equation 1 above:

x = 3 * 12/4

x = 36/4

x =

**9**

So our original fraction x/y =

**9/12**