Question

4/3(c+4) + 1 = 2c/(c+4)

Answer 1

c = (-29-5 i sqrt(15))/8 or c = (-29+5 i sqrt(15))/8

Answer 2

4/3(c+4) + 1 = 2c/(c+4)
4/3(c+4) - 2c/(c+4) + 1 = 0
[4 - 2c(3) +3(c+4)]/3(c+4) = 0
(4 - 6c +3c +12)/3(c+4) = 0
(-3c+16)/3(c+4) = 0 Multiply both sides by 3(c+4) to eliminate denominator
-3c+16 = 0
-3c = -16
c = 16/3

To verify if c=16/3 is correct substitute 16/3 for c for both the left side and right side of the equation:

4/3(c+4) + 1
4[(3)(16/3+4)+1=4/(16+12) + 1=4/28+1=1/7+1=8/7

2c/(c+4)
(2)(16/3)/(16/3+4)=(32/3)/(28/3)=(32/3)(3/28)=8/7