Question

the numerator of a fraction is 2 less than its denominator if 1 is added to both its numerator and denominator it becomes 2 /3 find the fraction​

Answer 1

Let the numerator be=x

Denominator= x+2

ATQ

x+1/x+2+1=2/3

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

3x+3=2x+6

3x-2x=6-3

x=3

Fraction =x+1/x+3

3+1/3+3

4/6=

2/3

Answer 2

let the fraction be x/y

let the numerator be x

let the denominator be y

according to the question

y-x=2 -(1)

x+1/y+1=2/3

or,3(x+1)=2(y+1)

or, 3x+3=2y+2

or, 3x-2y=2-3

or, 3x-2y=-1 -(2)

multiplying 2 in equation 1

adding equation 1 and 2

-2x+2y= 4

3x-2y=-1

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x=3

putting the value of x in equation (1)

y-x=2

y-3=2

y=2+3

y=5

fraction = x/y = 3/5