Question

the numerator of a fraction is 2 less than the denominator denominator if 1 is added to both numerator and denominator the sum of new and original fraction is 19 upon 15 find the original fraction

Answer 1

Answer:

3/5

Step-by-step explanation:

let the fraction be x/y

the numerator of a fraction is 2 less than the denominator

x=y-2

then the fraction will be (y-2)/y

if 1 is added to both numerator and denominator ⇒ (y-2+1)/(y+1)=(y-1)/(y+1)

the sum of new and original fraction is 19 upon 15

(y-2)/y + (y-1)/(y+1) = 19/15

((y-2)(y+1)+y(y-1)) / y(y+1)=19/15

(y²-y-2+y²-y) 15 = 19 (y²+y)

(2y²-2y-2)15 = 19y²+19y

30y²-30y-30-19y²-19y=0

11y²-49y-30=0

roots are 110/22 and -12/22

we should take only +ve values then 110/22=5

fraction is 3/5