The numerator of a fraction is 3 less than its denominator. If the numerator is increased by 1
and the denominator is increased by 3, the fraction becomes 1/2. Find the original fraction.​

Respuesta :

Answer:

[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

let x represent the denominator then x - 3 represents the numerator.

Increase the numerator by 1, that is x - 3 + 1 = x - 2

Increase the denominator by 3, that is x + 3, then fraction

[tex]\frac{x-2}{x+3}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2(x - 2) = x + 3, that is

2x - 4 = x + 3 ( subtract x from both sides )

x - 4 = 3 ( add 4 to both sides )

x = 7

Thus original fraction is

[tex]\frac{7-3}{7}[/tex] = [tex]\frac{4}{7}[/tex]