Answer:
[tex]\frac{2}{15}[/tex]
Step-by-step explanation:
Let the original fraction be [tex]\frac{x}{y}[/tex]
Then adding 1 to the numerator gives
[tex]\frac{x+1}{y}[/tex] = [tex]\frac{1}{5}[/tex] ( cross- multiply )
⇒ y = 5x + 5 → (1)
Subtracting 1 from the denominator gives
[tex]\frac{x}{y-1}[/tex] = [tex]\frac{1}{7}[/tex] (cross- multiply )
y - 1 = 7x → (2)
Substitute y = 5x + 5 into (2)
5x + 5 - 1 = 7x ← subtract 5x from both sides
4 = 2x ⇒ x = 2
Substitute x = 2 into (1)
y = (5 × 2) + 5 = 10 + 5 = 15
Hence original fraction = [tex]\frac{2}{15}[/tex]
