I need help solve the equation by fractions

Question

8/(21-y) = 12/(y+19)

I think the answer is y = 5, i just need to know how to do work out. i done some solution like this

first multiply by(21-y)(y+19)(assuming that y = 21 and y = 19:

(21-y)(y+19)8/(21-y) = (21-y)(y+19)12/(y+19)

then cancel and multiply out the brackets:

8(y+19) = 12(21-y)

that is

8x+152 = 12x-96

finally,rearrange the equation as

160x = 104

Answer 1

y=5 is correct.
To multiply by (21-y)(y+19), y must not equal 21 nor -19.

Correct until
8(y+19) = 12(21-y)
Expand:
8y+152=-12y+252
20y=100
y=5