Final answer:
To find the expression that makes (x+3)/(x²-8x+12)-:(x+3)/(x²+3x-10), simplify the expression and find the common denominator.
Step-by-step explanation:
To find the expression that makes (x+3)/(x²-8x+12)-:(x+3)/(x²+3x-10), we need to simplify the expression and then find the common denominator. Let's start by simplifying the expression:
(x+3)/(x²-8x+12)-:(x+3)/(x²+3x-10)
We can rewrite the division as multiplication by the reciprocal:
(x+3)/(x²-8x+12) * (x²+3x-10)/(x+3)
Next, we can factor the denominators:
(x+3)/(x-6)(x-2) * (x-2)(x+5)/(x+3)
Now, we can cancel out the common factors:
(x+3)/(x-6) * (x+5)
The expression that makes the original expression equal to this simplified expression is (x+5)/(x-6).