Question: If only one term is the 4e: 2 2 e what is the GCF in adding and subtracting rational expression with denominator

1. **State the problem:** We want to find the Greatest Common Factor (GCF) when adding or subtracting rational expressions where one term is $4e$, and the other terms involve $2$, $2$, and $e$. 2. **Recall the definition:** The GCF of terms is the largest expression that divides each term without leaving a remainder. 3. **Identify the terms:** The terms given are $4e$, $2$, $2$, and $e$. 4. **Factor each term:** - $4e = 2 \times 2 \times e$ - $2 = 2$ - $e = e$ 5. **Find common factors:** - The number $2$ appears in $4e$ and $2$. - The variable $e$ appears in $4e$ and $e$. 6. **Determine the GCF:** - The common numerical factor is $2$. - The common variable factor is $e$ (only if all terms have $e$). Since not all terms have $e$ (two terms are just $2$), the GCF only includes the common numerical factor $2$. 7. **Conclusion:** The GCF of the terms $4e$, $2$, $2$, and $e$ when adding or subtracting rational expressions is $2$. **Final answer:** $$\boxed{2}$$