Solve the equation and show steps? dots are to split up the problems.?

Question

4w – 1........ w-1 ...... w-1
_____ ......... - __ ....... = __
3w + 6 ......... 3 ....... w + 2

Answer 1

I guess you have to add these numbers, you need all component to have same common value.
your common value is:
X = (3w+6)*(3)*(w+2) = (3w + 6) ^2 = 9w^2 + 12w + 36, you miltiply each component with the other two values/ devided by thirself (equals to 1):
1. (4w-1)/(3w+6) * (3)*(w+2) / (3) / (w+2) = (4w-1) * (3w+6) / X
2. (w-1)/3 * (3w+6) * (w+2) / (3w+6) / (w+2) = (w-1) * (3w+6) * (w+2)/X
3. (w-1)/(w+2) * (3w+6) * 3 / (3w+6) / 3 = (w-1) * (3w+6) * 3 / X
now that each component have same common value you can add them
[(4w-1)*(3w+6) - (w-1)*(3w+6) + (3w-3)*(3w+6)] / X =
(3w+6) * [3w+6 - w +1 + 3w - 3] / X = (3w+6) * (5w+4) / X =
(5w+4) / (3w+6)

Answer 2

(4w - 1) / 3.(w + 2) - (w - 1)/3 = (w - 1)/(w + 2)
4w - 1 - (w - 1).(w + 2) = 3w - 3
4w - 1 - (w² + w - 2) = 3w - 3
4w - 1 - w² - w + 2 = 3w - 3
w² - 4 = 0
w = 2, w = - 2