The numerator of a fraction is three less than the denominator.What is the fraction if the numerator is tripled and denominator is increased by 7 ,...

According to enunciation, we'll put the denominator as x
and the numerator as x-3.

If we'll triple the numerator,
we'll get:

3(x-3) (1)

If we'll
increase the denominator by 7, we'll have:

x + 7
(2)

We'll divide (1) by (2) and we'll get
3/2:

3(x-3)/(x + 7) =
3/2

We'll divide by 3 both
sides:

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

We'll cross multiply and we'll
get:

x+7 = 2(x-3)

We'll remove
the brackets:

x + 7 = 2x -
6

We'll subtract 2x both
sides:

-x +7 = -6

We'll
subtract 7 both sides:

-x =
-13

We'll multiply by -1:

x =
13

Since the original ratio was (x-3)/x, we'll substitute x
and we'll calculate the value of the original
ratio:

(x-3)/x =
(13-3)/13

(x-3)/x =
10/13