Answer:
[tex]\frac{23}{30}[/tex]
Step-by-step explanation:
let the denominator of the original fraction be x, then
[tex]\frac{x-7}{x}[/tex] ← is the original fraction
After the given changes, that is
[tex]\frac{3(x-7)}{x+16}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
6(x - 7) = 3(x + 16) ← distribute parenthesis on both sides
6x - 42 = 3x + 48 ( subtract 3x from both sides )
3x - 42 = 48 ( add 42 to both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Thus
[tex]\frac{30-7}{30}[/tex] = [tex]\frac{23}{30}[/tex] ← the original rational number
