Since GE bisects the angle, we can use the angle bisector theorem
DE/EF = GD/GF
x-3/(x+1) = (x+3)/(x+10)
using cross products
(x-3) (x+10) = (x+1) (x+3)
FOIL
x^2 -3x+10x-30 = x^2 +x+3x+3
combine like terms
x^2 +7x-30 = x^2 +4x+3
subtract x^2 from each side
7x-30 = 4x+3
subtract 4x from each side
3x-30 = 3
add 30 to each side
3x =33
divide by 3
x=11
DF = (x-3+ (x+1)+
DF = 2x-2
= 2(11) -2
= 22-2
= 20
