Solve for x(problem includes fractions and imaginary)

**Thanasi** · October 12th 2009, 10:40 AM

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

**e^(i*pi)** · October 12th 2009, 10:48 AM

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

$<br /> \frac{1}{x-2} = \frac{3}{x+2} - \frac{6x}{(x-2)(x+2)}$

$<br /> \frac{x+2}{(x+2)(x-2)} = \frac{3(x-2)}{(x-2)(x+2)} - \frac{6x}{(x-2)(x+2)}$

The denominator cancels

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

$x = -2$

That's unusual...

**earboth** · October 12th 2009, 10:48 AM

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: $D = \mathbb{R} \setminus \{-2, 2\}$

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

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