1. **State the problem:** We need to find a fraction where the denominator is 3 less than the numerator. 2. **Define variables:** Let the numerator be $x$. Then the denominator is $x - 3$. 3. **Write the fraction:** The fraction is $\frac{x}{x-3}$. 4. **Use the given condition:** Increasing the numerator by 4 and decreasing the denominator by 3 gives the number 3. This means: $$\frac{x + 4}{(x - 3) - 3} = 3$$ 5. **Simplify the denominator:** $$(x - 3) - 3 = x - 6$$ So the equation becomes: $$\frac{x + 4}{x - 6} = 3$$ 6. **Solve the equation:** Multiply both sides by $x - 6$: $$x + 4 = 3(x - 6)$$ Expand the right side: $$x + 4 = 3x - 18$$ 7. **Isolate $x$:** $$4 + 18 = 3x - x$$ $$22 = 2x$$ Divide both sides by 2: $$x = 11$$ 8. **Find the denominator:** $$x - 3 = 11 - 3 = 8$$ 9. **Write the fraction:** $$\frac{11}{8}$$ **Final answer:** The fraction is $\frac{11}{8}$.