Simplify .

Question

Simplify .

BlackTom AI · Accepted Answer

The provided data for this item is incomplete. There are no answer options listed to analyze, and the stated 'answer' appears to be a fragment that resembles a potential choice label and a simplified form, but without the corresponding multiple-choice options we cannot evaluate which option is correct or why.

What we can do is outline a general approach to a simplification problem, and then show how to handle a typical fraction like (7x−1)/[(x−1)(x+1)].

General approach to a simplification problem:
- If you have an expression that is a fraction, look for common factors in the numerator and denominator that can cancel. Only factors that appear in both can be canceled, keeping in mind domain restrictions (e.g., you cannot cancel a factor that would make the denominator zero).
- If you have a polynomial in the numerator, check if it shares a factor with any factor in the denominator after factoring both. Do not attempt to cancel unless there is an exact common factor.
- If no common factors exist, the fraction is already in simplest form.
- Always note any restrictions on the variable (for example, x ≠ 1 and x ≠ −1 if the denominator contains (x−1)(x+1)).

Applying this to a typical expression like (7x−1)/[(x−1)(x+1)]:
- Factorization: The denominator factors as (x−1)(x+1). The numerator 7x−1 does not share a factor with (x−1) or (x+1) in a way that would yield cancellation, since 7x−1 is not a multiple of (x−1) or (x+1).
- Cancellation: There are no common factors between the numerator and denominator, so no cancellation is possible.
- Result (in simplest form): (7x−1)/[(x−1)(x+1)], with domain restrictions x ≠ 1 and x ≠ −1.

If you can provide the complete list of answer options, I can tailor the reasoning for each option and explain exactly why each one is correct or incorrect.

MATHS 108 Quiz 1 - The Diagnostic Quiz

Simplify .

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