To simplify the expression (4x² – 25) / (4x – 5), we need to start by factoring the numerator.
The expression in the numerator, 4x² – 25, is a difference of squares. It can be factored as:
- 4x² – 25 = (2x)² – (5)²
- Thus, it factors to: (2x – 5)(2x + 5)
So we can rewrite the expression as:
(2x – 5)(2x + 5) / (4x – 5)
Next, let’s simplify. We’re going to rewrite the denominator as:
4x – 5 = 2(2x – 5)
Now we rewrite the entire expression:
[(2x – 5)(2x + 5)] / [2(2x – 5)]
We can see that (2x – 5) is a common factor in both the numerator and the denominator.
Assuming 2x – 5 ≠ 0 (which we need to keep in mind to avoid division by zero), we can cancel (2x – 5):
=[(2x + 5) / 2]
Thus, the simplified form of the expression (4x² – 25) / (4x – 5) is:
(2x + 5) / 2