The denominator of a fraction is three more than twice the numerator. if both the numerator and denominator are decreased by one, the simplified result is 7/16. find the original fraction

15/33

Step-by-step explanation:

Let x represent the numerator of the original fraction. Then that fraction is ...

... x/(2x+3)

Decreasing numerator and denominator by 1 gives ...

... (x-1)/(2x +3 -1) = 7/16

Multiplying by the product of the denominators, we get ...

... 16(x -1) = 7(2x +2)

... 16x -16 = 14x +14 . . . . eliminate parentheses

... 2x = 30 . . . . . . . . . . . add 16-14x

... x = 15 . . . . . . . . . . . . divide by 2

And the original fraction is

... 15/(2·15+3) = 15/33

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.