((2/(x-2))+(2/(x^2 -4)))=(3/(x+2))

Question

please solve using i. Also, please explain the steps taken to solve the problem.

Answer 1

2/(x-2)+2/(x²-4)=3/(x+2), since x²-4=(x-2)(x+2):

(2(x+2)+2)/[(x-2)(x+2)]=3/(x+2) because 2/(x-2)=2(x+2)/[(x-2)(x+2)].

If we multiply both sides by x+2 (assuming x≠-2), we get:

(2x+4+2)/(x-2)=3, so 2x+6=3(x-2) (multiplying both sides by x-2),

2x+6=3x-6,

6+6=3x-2x,

12=x, so x=12 is the answer.

CHECK

Substituting x=12 in the original question:

LHS: 2/10+2/140=1/5+1/70=14/70+1/70=15/70=3/14;

RHS: 3/(x+2)=3/14, so LHS=RHS, confirming x=12 as the answer.