Question

operations with rational expressions: foundations
which of the following expressions is equivalent to \\(\frac{72}{-24x - 8}\\) ?
choose 1 answer:
a \\(\frac{9}{3x + 1}\\)
b \\(\frac{9}{-3x - 1}\\)
c \\(\frac{9}{-3x + 1}\\)
d \\(\frac{9}{-3x - 8}\\)
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Explanation:

Step1: Factor out the greatest common factor (GCF) from the denominator.

The denominator is \(-24z - 8\). The GCF of \(24\) and \(8\) is \(8\), and we can factor out \(-8\) (to make the leading coefficient positive in the factored form for easier comparison). So, \(-24z - 8=-8(3z + 1)\). Now the expression becomes \(\frac{72}{-8(3z + 1)}\).

Step2: Simplify the fraction by dividing the numerator and the denominator by their GCF.

The GCF of \(72\) and \(8\) is \(8\). Divide \(72\) by \(8\) and \(-8\) by \(8\): \(\frac{72\div8}{-8\div8(3z + 1)}=\frac{9}{-1(3z + 1)}\).

Step3: Distribute the negative sign in the denominator.

Distribute the \(-1\) in the denominator: \(\frac{9}{-3z - 1}\).

Answer:

B. \(\frac{9}{-3z - 1}\)