(x-2)/(x+4)-5/6=0

This might be easier Tetration

(x-2)/(x+4)-5/6=0 

 

$$\frac{x-2}{x+4}=\frac{5}{6}$$

 

 (You should be aware that x cannot equal -4)

 Multiply both sides by 6(x+4)  That will get rid of all the fractions. 

6(x-2)=5(x+4)

6x-12=5x+20

x=32

(x-2)/(x+4)-5/6=0     Add 5/6 to both sides:

 

(x - 2)/(x + 4) = 5/6      Multiply both sided by x + 4:

 

x - 2 = 5(x + 4)/6          

 

x - 2 = (5x + 20)/6 = 5x/6 + 10/3      

 

x - 5x/6 = 10/3 +2                Get common denominator (bottom) by x = 1x/1 = 6x/6:

 

6x/6 - 5x/6 = 10/3 + 6/3       

 

x/6 = 16/3                            Multiply both sides by 6 = 2*3:

 

x = (16*2*3)/3 = 16*2 = 32