Question

100 POINTS

The numerator is 2 less than the denominator. If I add 3 both to the numerator and the denominator, the answer would be 5/6. what's the original fraction? ​

Answer 1

`(7)/(9)`

Explanation:

Let x be the denominator.

If the numerator is 2 less than the denominator, then the expression for the numerator is (x - 2):

`(x-2)/(x)`

If 3 is added to both the numerator and the denominator, and the answer is 5/6, then:

`(x-2+3)/(x+3)=(5)/(6)`

Now we can solve the equation for x.

Simplify the numerator in the fraction on the left of the equation:

`(x+1)/(x+3)=(5)/(6)`

Cross mutliply:

`6(x+1)=5(x+3)`

Expand the brackets:

`6 \cdot x +6 \cdot 1 = 5 \cdot x + 5 \cdot 3`

`6x+6=5x+15`

Subtract 5x from both sides of the equation:

`6x+6-5x=5x+15-5x`

`x+6=15`

Subtract 6 from both sides of the equation:

`x+6-6=15-6`

`x=9`

Therefore, the value of x is 9.

Now substitute the found value of x into the original rational expression:

`(x-2)/(x)=(9-2)/(9)=(7)/(9)`

Therefore, the original fraction is:

`\boxed{(7)/(9)}`