8. The denominator of a fraction exceeds the numerator by 4 . When 3 is added to both the numerator and the denominator, the fraction becomes \( \frac{4}{5} \). Find the fraction. (Please solve by using algebraic method)

Let's denote the numerator as \( x \). Therefore, the denominator will be \( x + 4 \) since it exceeds the numerator by 4. The original fraction can be written as: \[ \frac{x}{x + 4} \] According to the problem, when we add 3 to both the numerator and the denominator, the fraction becomes \( \frac{4}{5} \): \[ \frac{x + 3}{(x + 4) + 3} = \frac{x + 3}{x + 7} = \frac{4}{5} \] Now, we can cross-multiply to eliminate the fraction: \[ 5(x + 3) = 4(x + 7) \] Expanding both sides gives: \[ 5x + 15 = 4x + 28 \] Now, let's isolate \( x \) by subtracting \( 4x \) from both sides: \[ 5x - 4x + 15 = 28 \] This simplifies to: \[ x + 15 = 28 \] Next, subtract 15 from both sides: \[ x = 13 \] Now that we have the numerator, we can find the denominator: \[ x + 4 = 13 + 4 = 17 \] Thus, the fraction is: \[ \frac{13}{17} \]