Question

match the following items with their descriptions for simplifying the following rational expression: $\frac{7x - 35}{14x^{2}}$ 3. write in simplest terms 7 is common between numerator and denominator 1. determine gcf $\frac{x - 5}{2x^{2}}$ 2. determine common factor(s) to reduce $\frac{7(x - 5)}{14x^{2}}$

Explanation:

Step1: Factor the numerator

Factor out 7 from \(7x - 35\) to get \(7(x - 5)\), so the rational - expression becomes \(\frac{7(x - 5)}{14x^{2}}\).

Step2: Determine the GCF

The GCF of 7 and 14 is 7. So, 7 is a common factor between the numerator and the denominator.

Step3: Simplify the expression

Divide both the numerator and the denominator by 7. \(\frac{7(x - 5)\div7}{14x^{2}\div7}=\frac{x - 5}{2x^{2}}\).

Answer:

1. Determine GCF: 7 is common between numerator and denominator
2. Determine common factor(s) to reduce: \(\frac{7(x - 5)}{14x^{2}}\)
3. Write in simplest terms: \(\frac{x - 5}{2x^{2}}\)