if x,y,z are positive numbers and xy + x + y = 23 ; xz + x + z = 41; yz + y + z = 27, find x + y + z

xy + x + y = 23
xy+x+y+1=24
(x+1)(y+1)=24..........................1
xz + x + z = 41
xz + x + z + 1 = 42
(x+1)(z+1) = 42..............2
yz + y + z +1 = 28
(y+1)(z+1) = 28...................3
from 1, 2 & 3 ony x=5,y=3 and z=6 satisfy the given equations therefore
x + y + z=14