Answer:
[tex]\frac{29}{58}[/tex]
Step-by-step explanation:
let x be the numerator of the rational number then 2x is the denominator
original fraction = [tex]\frac{x}{2x}[/tex]
subtracting 3 from numerator and adding 7 to denominator , gives
[tex]\frac{x-3}{2x+7}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )
5(x - 3) = 2(2x + 7) ← distribute parenthesis on both sides )
5x - 15 = 4x + 14 ( subtract 4x from both sides )
x - 15 = 14 ( add 15 to both sides )
x = 29
rational number = [tex]\frac{29}{58}[/tex]
