Respuesta :
Step-by-step explanation:
(1)
Let the numerator be x and denominator be y. A/Q x + y = 4 + 2x → - x + y = 4
(2)
multiplying each term by 2, 2x-2y= -8
(3)
Also, (x+3) / (y+3) = 2 / 3 → 3x - 2y = -3
Subtracting (2) from (3) → x = 5 and by putting this in (1) we can get y=9. Hence, the fraction is 5 / 9
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
let the fraction be [tex]\frac{x}{y}[/tex], then
x + y = 2x + 4 ( subtract x from both sides )
y = x + 4 → (1)
If 3 is added to numerator and denominator, then
[tex]\frac{x+3}{y+3}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3(x + 3) = 2(y + 3) ← distribute both sides
3x + 9 = 2y + 6 ← substitute y = x + 4
3x + 9 = 2(x + 4) + 6
3x + 9 = 2x + 8 + 6 = 2x + 14 ( subtract 2x from both sides )
x + 9 = 14 ( subtract 9 from both sides )
x = 5
Substitute x = 5 into (1)
y = 5 + 4 = 9
Hence the original fraction is [tex]\frac{5}{9}[/tex]
