Question

The numerator of a fraction is 3 less than its denominator. If 2 is added to both to the numerator and the denominator, then the sum of the new fraction and original fraction is29/30 find the original faction

Answer 1

QUESTION


The numerator of a fraction is 3 less than its denominator. If 2 is added to both to the numerator and the denominator, then the sum of the new fraction and original fraction is 29/30 find the original fraction.

Solution is here:

Let the denominator be x
so the Numerator  will be 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

x = -12/11 or x = 10

since it can't be negative. so

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

Thank you

@Be Brainly

Answer 2

hey user!!

we are given that the numerator of a fraction is 3 less that it's denominator.

let the denominator of the fraction be x. therefore the numerator of the fraction is x - 3

after adding 2 to both numerator and denominator :-

numerator = x - 3 + 2
x - 1

denominator = x + 2

therefore (x-1)/(x+2) = 29/30
>> 30(x-1) = 29(x+2)
>> 30x - 30 = 29x + 58
>> 30x - 29x = 58 + 30
>> x = 88

hence, denominator of the fraction = x = 88
and numerator = x - 3 = 88 - 3 = 85

verification :-

LHS :-

= (x - 3 + 2)/x+2
= (85 + 2)/88 + 2
= 87/90
= 29/30

RHS :-

= 29/30

hence, LHS = RHS

cheers!!!