How to solve x-2/x + 1/3 + -2x/x-4 using simplification of fractions using addition and subtraction?

To solve the expression x-2/x + 1/3 + -2x/x-4 using simplification of fractions through addition and subtraction, follow these steps:

1. Find a common denominator for all the fractions in the expression. In this case, the common denominator is 3(x)(x-4).

2. Rewrite each fraction with the common denominator:
x-2/x = 3(x-2)/3(x)
1/3 = (x-4)/3(x-4)
-2x/x-4 = -6(x)/3(x-4)

3. Add or subtract the fractions:
3(x-2)/3(x) + (x-4)/3(x-4) - 6(x)/3(x-4)

4. Combine the fractions by adding or subtracting the numerators:
(3(x-2) + (x-4) - 6(x))/3(x-4)

5. Simplify the expression:
(3x - 6 + x - 4 - 6x)/3(x-4)
(4x - 10 - 6x)/3(x-4)
(-2x - 10)/3(x-4)

Therefore, the simplified expression is -2x - 10 / 3(x-4).