The sum of the numerator and denominator of a fraction expressed in simplest form is 17. If 3 is added to the numerator, the value of the fraction will be 1. What is the fraction?

X+y=17 solve for a variable and plug into the 2nd equation

(x+3) / y=1 also could be written as x+3=y

x=17-y

17-y+3=y combine and add y over to other side

20=2y

y=10

plug back in x+10=17

x=7

so the original fraction is 7/10

X is represented as the numerator, y is the denominator.

x+y=17

x+3/y = 1

If x+3/y is 1, x+3 must equal y. Use the first equation to solve for y.

y=17-x

Plug in the first equation.

x+3 = y

x+3 = 17-x

x+3+x=17-x+x (Add x)

2x+3=17

2x+3-3=17-3 (subtract 3)

2x=14

x=7.

Plug in x into original equation (x+y=17)

7+y=17

y=10

The fraction is 7/10.