2/(3x)+4/x=7/(x+1) How would I solve something like this?

2/(3x)+4/x=7/(x+1)    getting a common denominator on the left. we have

[2x + 12x] / [3x²] = 7/(x+1)      and cross- multiplying, we have

[ 14x]*[x + 1 ] = 21x² 

x (x + 1) = 3x²

x² + x = (3/2)x²     rearranging, we have

(1/2)x² - x = 0       multiply by 2 on both sides

x² - 2x = 0             factor

x(x -2) = 0   

Then x = 0  or x =2      reject 0, since it makes the two denominators in the original problem undefined

So .....  x = 2