To solve this complex fraction equation, we need to get the same denominator on the left, then combine them to one term. Then we can cross-multiply with the other side.
1/2 + 4/2x = x/2x + 4/2x = (x+4)/2x
Now we have (x+4)/2x = (x+4)/10
cross-multiply:
(x+4)×10 = (x+4)×2x
10x+40 = 2x^2+8x
[tex]2 {x}^{2} + 8x - 10x - 40 = 0 \\ 2 {x}^{2} - 2x - 40 = 0 \\ 2({x}^{2} - x - 20) = 0 \\ 2(x - 5)(x + 4) = 0 [/tex]
Therefore x = -4 and x = 5
C) is the correct answer
