# Thread: Solve for x(problem includes fractions and imaginary)

1. ## Solve for x(problem includes fractions and imaginary)

That's the problem. I got an answer of -2 which I am not sure of. Help me please.

2. Originally Posted by Thanasi

That's the problem. I got an answer of -2 which I am not sure of. Help me please.
-2 does not lie in the domain of this function as it causes division by 0 on the RHS

$\displaystyle \frac{1}{x-2} = \frac{3}{x+2} - \frac{6x}{(x-2)(x+2)}$

$\displaystyle \frac{x+2}{(x+2)(x-2)} = \frac{3(x-2)}{(x-2)(x+2)} - \frac{6x}{(x-2)(x+2)}$

The denominator cancels

$\displaystyle x+2 = 3x-6-6x$

$\displaystyle x = -2$

That's unusual...

3. Originally Posted by Thanasi

That's the problem. I got an answer of -2 which I am not sure of. Help me please.
1. Determine the domain of this equation: $\displaystyle D = \mathbb{R} \setminus \{-2, 2\}$

2. Then solve the equation. You'll get x = -2 BUT this value isn't in the domain. Therefore this equation has no solution.