# Solve for x(problem includes fractions and imaginary)

• October 12th 2009, 11:40 AM
Thanasi
Solve for x(problem includes fractions and imaginary)
http://i36.tinypic.com/24azvvo.jpg

That's the problem. I got an answer of -2 which I am not sure of. Help me please.
• October 12th 2009, 11:48 AM
e^(i*pi)
Quote:

Originally Posted by Thanasi
http://i36.tinypic.com/24azvvo.jpg

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

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

$
\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...
• October 12th 2009, 11:48 AM
earboth
Quote:

Originally Posted by Thanasi
http://i36.tinypic.com/24azvvo.jpg

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.