What is the original fraction?

Question

In a certain fraction, the denominator is 2 less than the numerator. If 1 is added to both the numerator and denominator, the resulting fraction is equal to 9/7. what is the original fraction?

Answer 1

d = denominator

n = numerator

 

d = n-2

 

Original Fraction:  n/(n-2)

 

Add 1 to numerator and denominator and set equal to 9/7

 

(n+1)/(n-1) = 9/7

 

n+1 = 9 and n-1 = 7

n = 8

 

Original fraction:  n/(n-2) = 8/6

Answer 2

d = n-2

(n+1)/(d+1) = 9/7

 

Let's simplify that second equation in terms of d.

 

(n+1)/(d+1) = 9/7

7(n+1) = 9(d+1)

7n + 7 = 9d + 9

7n - 2 = 9d

(7n-2)/9 = d

 

So now we have 2 equations equal to d, so we can use them to solve for n.

 

n - 2 = (7n-2)/9

9(n-2) = 7n -2

9n - 18 = 7n-2

2n = 16

n=8

 

d = n-2

d = 8-2

d=6

 

To check our answer, we can now plug these back into the other equation:

(n+1)/(d+1) = 9/7

(8+1)/(6+1) = 9/7

9/7 = 9/7

 

So the original fraction would be 8/6.