Answer:
x=0, 2/3
Step-by-step explanation:
x/4 = x^2 /(x+2)
Using cross products
4x^2 = x(x+2)
Distribute
4x^2 = x^2 +2x
Subtract x^2 from each side
3x^2 = 2x
Subtract 2x from each side
3x^2 -2x =0
Factor out x
x(3x-2) =0
Using the zero product property
x=0 3x-2 =0
x=0 3x=2
x=0 x= 2/3
Check
x=0
0/4 = 0^2 /(0+2)
0 = 0
Check
x=2/3
(2/3)/4 = (2/3)^2 /((2/3)+2)
1/6 = (4/9)/ (8/3)
1/6 = 4/9 * 3/8
1/6 = 4/8 *3/9
1/6 = 1/6
Both solutions are valid
