Question

The numerator of a fraction is 3 less than denominator. If 2 is added to both numerator as well as denominator, then sum of the new and original fraction is 29/20. Find the 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

Answer:

(x-3)/x=7/10

Step-by-step explanation:

                   

Let the denominator be x

             

So, Numerator  is x-3

                     

We got fraction,

$\frac{x}{x-3}$

                                 

                   According to question, when 2 is added to numerator and denominator,

Then, we get = (x-1)/(x+2)

                     

So,

=> (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

                       

We will have to cancel the negative fraction value  of x.

=> X = 10

                             

We have the fraction,

=> (x-3)/x=7/10