Final answer:
To subtract (9a/a²-5a-6) from (54/a²-5a-6) and simplify, we directly subtract the numerators over the common denominator and then simplify. The result is 9(a - 6)/(a² - 5a - 6). We then check for further simplification by trying to factor the denominator and cancel any common terms.
Step-by-step explanation:
To subtract the fractions (9a/a²-5a-6) - (54/a²-5a-6) and simplify the result if possible, we notice that the denominator is the same for both fractions, which allows for direct subtraction of the numerators.
The subtraction looks like this:
9a - 54, which we then simplify over the common denominator a² - 5a - 6.
The simplified form of the numerator is 9a - 54 = 9(a - 6). We can then place this over the common denominator, which gives us the simplified expression:
9(a - 6)/(a² - 5a - 6). Checking the result, we can determine if it's reasonable by evaluating whether the expression is fully simplified or if any further factorization is possible.
If the quadratic in the denominator can be factored, it should be done, and any common factors with the numerator should be canceled out for full simplification.