Question

the number of the fraction is 3 less than the denominator if the number is increased by 1 and the denominator is increased by 3 the fraction becomes half find the original fraction

Answer 1

Heya !!!


Let the denominator of the fraction be X.


Numerator or the fraction = (X-3)



Fraction = Numerator/Denominator = (X-3)/X


Numerator is increased by 1 = (X-3+1) = (X-2)



And,

Denominator is increased by 3 = (X+3)




Fraction = Numerator/Denominator = (X-2)/(X+3)



According to question,



(X-2)/(X+3) = 1/2 × (X-3)/ X


X-2 / X +3 = X-3 / 2X



2X(X-3) = (X+3) (X-3)


2X² - 6X = (X)² - (3)²


2X² - X² -6X + 9 = 0


X² - 6X + 9 = 0


X² -3X - 3X + 9 = 0


X(X-3) -3 ( X -3) = 0

(X-3) ( X -3) = 0


(X-3) = 0


X = 3


Denominator of Fraction = X = 3



and,

Numerator of fraction = X -3 = 3 -3 = 0



Fraction = Numerator/Denominator = 0/3




HOPE IT WILL HELP YOU....... :-)