simplify the following
x^2/x^2-x-12 - x-2/x-3
To simplify the expression, we will factor the denominators and find the least common denominator.
Step 1: Factor the denominator x^2 - x - 12
(x^2 - x - 12) can be factored as (x - 4)(x + 3).
Step 2: Factor the denominator x - 3
(x - 3) cannot be factored further.
The least common denominator is (x - 4)(x + 3).
Step 3: Perform the subtraction in the numerators
x^2 - x - 12 - (x - 2)
= x^2 - x - 12 - x + 2
= x^2 - 2x - 10
Now we have the simplified numerator and the simplified least common denominator:
Numerator: x^2 - 2x - 10
Denominator: (x - 4)(x + 3)
Putting it all together, the expression simplifies to:
(x^2 - 2x - 10) / (x - 4)(x + 3)