Complex Fractions?

Question

Please show me in step by step one by one with clean space between your text and lines. This is probably a simple solution, but I like to see how many different ways you can approach this:- Thanks

s/(3s+2) + (s+3)/(2s-4) = -2s/(3s+2)(s-2)

Answer 1

LHS
s /(3s + 2) + (1/2).(s + 3) / (s - 2)
RHS
- 2s / (3s + 2).(s - 2)
Multiply both sides by (3s + 2).(s - 2)
LHS becomes:-
s.(s - 2) + (s + 3)(3s + 2) / 2
RHS becomes:-
- 2s

s.(s - 2) + (s + 3) (3s + 2) / 2 = - 2s
s² - 2s + (3s² + 11s + 6) / 2 = - 2s
2s² - 4s + 3s² + 11s + 6 = - 4s
5s² + 11s + 6 = 0
(5s + 6).(s + 1) = 0
s = - 6 / 5, s = - 1

Answer 2

s/(3s+2) + (s+3)/(2s-4) = -2s/(3s+2)(s-2)
multiply equation by 3s+2
s + (3s+2)(s+3)/(2s-4)=-2s/(s-2)
multiply equation by 2s-4
s(2s-4) + (3s+2)(s+3) = -2s(2s-4)/(s-2)
multiply exuation by s-2
s(2s-4)(s-2) + (3s+2)(s+3)(s-2) = -2s(2s-4).
multiplying terms
s(2s^2-8s+8) + (3s+2)(s^2+s-6) = -4s^2+8s
2s^3-8s^2+8s + 3s^3+5s^2-16s-12 = -4s^2+8s.
gathering like terms
5s^3+s^2-16s-12 = 0
(s-2)(5s^2+11s+6) = 0
(s-2)(5s+6)(s+1) = 0
s = 2, .-1, -1.2