First, we each side of the equation by a common denominator (in this case #8(x - 2)#) to eliminate the fraction and keep the equation balanced:
#8(x - 2) (x + 2)/(x - 2) = 8(x - 2) 4/8#
#8cancel((x - 2)) (x + 2)/cancel((x - 2)) = cancel(8)(x - 2) 4/cancel(8)#
#8(x + 2) = 4(x - 2)#
Now we can expand the terms in parenthesis on each side of the equation:
#8x + 16 = 4x - 8#
Next we can isolate the #x# terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:
#8x + 16 - 16 - 4x = 4x - 8 - 16 - 4x#
#8x + 0 - 4x = 0 - 24#
#8x - 4x = -24#
#4x = -24#
Finally, we can solve for #x# while keeping the equation balanced:
#(4x)/4 = (-24)/4#
#(cancel(4)x)/cancel(4) = -6#
#x = -6#
