Answer:
[tex]\frac{7}{26}[/tex]
Step-by-step explanation:
let x be the denominator of the fraction then x - 19 is the numerator , so
[tex]\frac{x-19}{x}[/tex] ← is the original fraction
subtrating 1 from the numerator and adding 1 to the denominator , then
[tex]\frac{x-20}{x+1}[/tex] = [tex]\frac{2}{9}[/tex] ( cross- multiply )
9(x - 20) = 2(x + 1) ← distribute parenthesis on both sides
9x - 180 = 2x + 2 (subtract 2x from both sides )
7x - 180 = 2 ( add 180 to both sides )
7x = 182 ( divide both sides by 7 )
x = 26
Then the original fraction is
[tex]\frac{26-19}{26}[/tex] = [tex]\frac{7}{26}[/tex]
