Question 7089
You could use this approach:

Let d = the denominator.

{{{((d-10)+4)/(d+4) = 3/5}}} Simplify then cross-multiply.

{{{(d-6)/(d+4) = 3/5}}}
{{{5(d-6) = 3(d+4)}}} Simplify and solve for d.
{{{5d-30 = 3d+12}}} Subtract 3d from both sides.
{{{2d-30 = 12}}} Add 30 to both sides.
{{{2d = 42}}} Divide both sides by 2.
d = 21

The original fraction is:
 {{{(d-10)/d}}} or
{{{(21-10)/21}}}
{{{11/21}}} This is the original fraction.

Check: 

Adding 4 to the numerator and to the denominator, we get:
{{{(11+4)/(21+4) = 15/25 = 3/5}}}