(x-1)/(x-3)/1/x2-x-6-4/(x+2)
To simplify the given expression, we need to combine the fractions by finding a common denominator. Let's break it down step by step:
1. Start by finding the common denominator for the fractions in the expression: (x-1)/(x-3) and 4/(x+2).
The denominators are (x-3) and (x+2), so the common denominator will be (x-3)(x+2).
2. Now, we can rewrite the expression with the common denominator:
[(x-1)/(x-3)] / [(1/(x-3))(x+2)] - [4/(x+2)] x (x-3)(x+2)
Note: To divide fractions, we multiply by the reciprocal of the second fraction.
3. Simplify further:
[(x-1)/(x-3)] / [(x+2)/(x-3)] - [4/(x+2)] x (x-3)(x+2)
4. Next, simplify the first fraction (division is equivalent to multiplying by the reciprocal):
[(x-1)/(x-3)] x [(x-3)/(x+2)] - [4/(x+2)] x (x-3)(x+2)
5. Cancel out common factors:
[(x-1)/(x+2)] - [4/(x+2)] x (x-3)(x+2)
6. Simplify further:
[(x-1)/(x+2)] - 4(x-3)
7. Expand and collect like terms:
(x-1) - 4x + 12
8. Combine like terms:
-3x + 11
Therefore, the simplified form of the expression is -3x + 11.