Final answer:
To simplify the expression (8a²-10a-3)/(4a²-9) by factorizing, the numerator (8a²-10a-3) can be factored as (4a+1)(2a-3), and the denominator (4a²-9) can be factored as (2a+3)(2a-3).
Step-by-step explanation:
To simplify the expression (8a²-10a-3)/(4a²-9) by factorizing, we can start by factoring the numerator and denominator separately.
The numerator, 8a²-10a-3, can be factored as (4a+1)(2a-3).
The denominator, 4a²-9, can be factored as (2a+3)(2a-3).
Therefore, we can cancel out the common factor (2a-3) in the numerator and denominator, leaving us with the simplified expression (4a+1)/(2a+3).