In a certain fraction, the denominator is 4 less than the numerator. if 3 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. what was the original fraction (not written in lowest terms?

Make a system of equation before finding the numbers. d stands for denominator and n stands for the numerator.

⇒ d = n - 4 (first equation)

⇒ (n + 3) / (d + 3) = 2 (second equation)

Simplify the second equation

(n + 3) / (d + 3) = 2

(n + 3) = 2 (d + 3)

n + 3 = 2d + 6

Solve the equation system by subtituting d with n-4 from the first equation into the second equation

n + 3 = 2d + 6

n + 3 = 2 (n - 4) + 6

n + 3 = 2n - 8 + 6

n + 3 = 2n - 2

n - 2n = - 2 - 3

-n = - 5

n = 5

The original numerator is 5

Find the original denominator by inputing 5 as numerator to one of the equation

d = n - 4

d = 5 - 4

d = 1

The original denominator is 1

So the original fraction is 5/1