Answer
The equation has no solutions.
Work Step by Step
STEP 1: Restrictions. There must be no zeros in the denominator, so
$x\neq\pm 2$
STEP 2: Fractions. The LCM of all denominators is $x^{2}-4=(x+2)(x-2).$
After multiplying both sides with the LCM,
$2x=4-3(x-2)$
STEP 3: Remove all parentheses and simplify.
$2x=4-3x+6$
$2x=10-3x$
STEP 4: Variables on one side, all other terms on the other...
$2x=10-3x\qquad/+3x$
$5x=10$
STEP 5: Simplify and solve.
$5x=10\qquad /\div 5$
$x=2$
In step 1, the number $2$ is excluded as a possible solution.
Thus, the equation has no solutions.
