To simplify the expression (x² – 15x + 36) / (5x – 60), we will start by factoring both the numerator and the denominator.
First, let’s factor the numerator:
- The expression is x² – 15x + 36.
- We need to find two numbers that multiply to 36 and add up to -15.
- These numbers are -3 and -12.
- Therefore, we can factor the numerator as:
- (x – 3)(x – 12)
Now, let’s factor the denominator:
- The expression is 5x – 60.
- We can factor out a 5 from both terms:
- 5(x – 12)
Now we can rewrite the entire expression:
(x – 3)(x – 12) / (5(x – 12))
Next, we notice that (x – 12) is a common factor in both the numerator and the denominator. We can cancel this factor, as long as x ≠ 12 (since division by zero is undefined).
This gives us:
(x – 3) / 5
So, the simplified form of the expression (x² – 15x + 36) / (5x – 60) is:
(x – 3) / 5, for x ≠ 12.