Question

The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simplified result is 1718

17


18


. Find the original fraction. (Do NOT simplify.)

Answer 1

`(40)/(42)`

Explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

`(x)/(x+2)`

If both numerator and denominator are decreased by six, the fraction becomes:

`(x-6)/(x+2-6)`

The simplified result is
`(17)/(18)`

Therefore:

`(x-6)/(x+2-6)=(17)/(18)\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40`

Substituting x=40 into the initial fraction

`(x)/(x+2)=(40)/(40+2)=(40)/(42)`

Therefore, the original fraction is
`(40)/(42)`