Solve
A.) X= 8a
B.) X=4a
C.) X=4a
D.) X=8a
A.) X= 8a
B.) X=4a
C.) X=4a
D.) X=8a

(2xa)/(x+a) (x+3a)/(ax)=a²/(a²x²) +3
[(2xa)(ax)(x3a)(x+a)]/(a²x²)=a²/(… +3
[2x²+3axa²(x²2ax3a²)]=a²+3(a²x²)
3x²+2a²+5ax=a²+3a²3x²
5ax=2a²
x=2/5 a
[(2xa)(ax)(x3a)(x+a)]/(a²x²)=a²/(… +3
[2x²+3axa²(x²2ax3a²)]=a²+3(a²x²)
3x²+2a²+5ax=a²+3a²3x²
5ax=2a²
x=2/5 a

fully factor everything.
assuming expression is
(2xa) / (x+a)  (x+3a)/(ax) = a^2/(a^2x^2) + 3
(2xa) / (a+x)  (x+3a)/(ax) = a^2/(ax)(a+x) + 3
lowest comon denominator: (xa)(x+a):
(2xa)(ax) / (ax)(a+x)  (x+3a)(a+x)/(ax)(a+x) = a^2/(ax)(a+x) + 3(ax)(a+x)/(ax)(a+x)
SINCE denominators are equal to each other, solve using numerators.
(2xa)(ax)  (3a+x)(a+x) = a^2 +3(ax)(a+x)
2x^2 +2ax ax a^2  (3a^2 +3ax +ax +x^2) = a^2 + 3(a^2 +ax ax x^2)
2x^2 +ax a^2 (3a^2 +4ax +x^2) = a^2 +3(a^2 x^2)
2x^2 +ax  a^2 3a^2 4ax x^2 = a^2 +3a^2 3x^2
x^2 4a^2 3ax = 4a^2 3x^2
0 = 4a^2 +4a^2 3x^2 x^2 +3ax
0 = 8a^2 +3ax  4x^2
use quadratic formula.
assuming expression is
(2xa) / (x+a)  (x+3a)/(ax) = a^2/(a^2x^2) + 3
(2xa) / (a+x)  (x+3a)/(ax) = a^2/(ax)(a+x) + 3
lowest comon denominator: (xa)(x+a):
(2xa)(ax) / (ax)(a+x)  (x+3a)(a+x)/(ax)(a+x) = a^2/(ax)(a+x) + 3(ax)(a+x)/(ax)(a+x)
SINCE denominators are equal to each other, solve using numerators.
(2xa)(ax)  (3a+x)(a+x) = a^2 +3(ax)(a+x)
2x^2 +2ax ax a^2  (3a^2 +3ax +ax +x^2) = a^2 + 3(a^2 +ax ax x^2)
2x^2 +ax a^2 (3a^2 +4ax +x^2) = a^2 +3(a^2 x^2)
2x^2 +ax  a^2 3a^2 4ax x^2 = a^2 +3a^2 3x^2
x^2 4a^2 3ax = 4a^2 3x^2
0 = 4a^2 +4a^2 3x^2 x^2 +3ax
0 = 8a^2 +3ax  4x^2
use quadratic formula.