solve the rational equation:(x^2-4)/(x+2)=(x-2)/(x+1)

Question

solution

Answer 1

((X-2)(X+2)/(X+2)=(X-2)/(X+1)

X-2=(X-2)/(X+1)

X+1=1

X=0

Answer 2

x²-4=(x-2)(x+2) so we have:

(x-2)(x+2)/(x+2)=(x-2)/(x+1). If x=2 this gives us: 0/4=0/3⇒0=0 which is true, so x=2 is a solution.

Next we remove the factor x-2: (x+2)/(x+2)=1/(x+1). If x≠-2: 1=1/(x+1), x+1=1⇒x=0, which is another solution.

SOLUTION: x=0 or 2.