The numerator of a fraction is 3 less than denominator if 2 is added to both numerator and denominator then the sum of original and new fraction is 29 /30 find the number
Answers
Answered by
2
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
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
Similar questions