Question

numerator of a fraction is 2 less than the denominator if 1 is added to the numerator and 3 to the denominator then the fraction became 2/3 find the original fraction​

Answer 1

Answer:

Let the numerator be x

Therefore, denominator is x+2

The fraction is

x+2

x

Now,

x+2

x

+

x+3

x+1

=

15

19

=>

(x+2)(x+3)

x

2

+3x+(x+1)(x+2)

=

15

19

=>

(x+2)(x+3)

x

2

+3x+x

2

+3x+2

=

15

19

=>15(x

2

+3x+x

2

+3x+2)=19(x+2)(x+3)

=>15(2x

2

+6x+2)=19(x

2

+5x+6)

=>30x

2

+90x+30=19x

2

+95x+114

=>11x

2

−5x−84=0

=>11x

2

−33x+28x−84=0

=>11x(x−3)+28(x−3)=0

=>(11x+28)(x−3)=0

Therefore, x=3 or x=−

11

28

For x=−

11

28

, denominator is :-

−

11

28

+2=

11

−28+22

=−

11

6

So, the fraction is

−

11

6

−

11

28

=

6

28

=

3

14

Now adding 1 on both numerator and denominator we get

4

15

But,

3

14

+

4

15



=

15

19

∴x=3 and denominator is x+2=3+2=5

∴ the fraction is 3/5