Question

the numerator of a fraction is 3 less than its denominator if 2 is added to both numerator and the denominator then the sum of a new fraction and version fraction is on 29 by 30 find the original fraction​

Answer 1

Let the denominator be x

Numerator is x-3

The fraction is (x-3)/x

when 2 is added to numerator and denominator

we have fraction as (x-1)/(x+2)

ATQ (x-3)/x +(x-1)/(x+2)= 29/20

⇒ (x-3)((x+2) +x(x-1)=x(x+2)*29/20

⇒ (x²-6-x + x²-x)20= 29x²+58x

⇒ 40x²-120-40x=29x²+58x

⇒ 11x²-98x- 120=0

⇒ 11x² - 110x +12x -120=0

⇒ (11x+12)(x-10)=0

Canceling the negative fraction value of x we have x=10

Then the fraction (x-3)/x=7/10

Answer 2

Numerator=x

denominator=x+3

x+(x+3)+4=29+30

2x+3+4=59

2x=59-3-4

2x=52

x=52÷2

x=26

numerator=x=26

denominator=x+3=26+3=29