Divide. Write your answer in simplest form. 14g - 7/g + 1 ÷ 3g + 5/3g ______

Identify Common Factors: Now, we look for common factors in the numerators and denominators that can be simplified. The numerator 14g - 7 can be factored as 7(2g - 1) because 14g = 7 * 2g and -7 = 7 * -1. The expression becomes (7(2g - 1))/(g + 1) * (3g)/(3g + 5).Multiply Numerators and Denominators: Next, we multiply the numerators together and the denominators together. Multiplying the numerators: 7(2g - 1) * 3g = 21g(2g - 1). Multiplying the denominators: (g + 1)(3g + 5). The expression now looks like this: (21g(2g - 1))/((g + 1)(3g + 5)).Check for Common Factors: We should check if there are any common factors between the numerator and the denominator that can be canceled out. However, there are no common factors between 21g(2g - 1) and (g + 1)(3g + 5), so the expression is already in its simplest form.Final Answer: The final answer is the expression we have after the multiplication, which is (21g(2g - 1))/((g + 1)(3g + 5)).

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Write your answer in simplest form.

\newline

\frac{14g - 7}{g + 1} \div \frac{3g + 5}{3g}

Identify Common Factors: Now, we look for common factors in the numerators and denominators that can be simplified. The numerator $14g - 7$ can be factored as $7(2g - 1)$ because $14g = 7 \times 2g$ and $-7 = 7 \times -1$ . The expression becomes $(7(2g - 1))/(g + 1) \times (3g)/(3g + 5)$ .
Multiply Numerators and Denominators: Next, we multiply the numerators together and the denominators together. $\newline$ Multiplying the numerators: $7(2g - 1) \times 3g = 21g(2g - 1)$ . $\newline$ Multiplying the denominators: $(g + 1)(3g + 5)$ . $\newline$ The expression now looks like this: $\frac{21g(2g - 1)}{(g + 1)(3g + 5)}$ .
Check for Common Factors: We should check if there are any common factors between the numerator and the denominator that can be canceled out. $\newline$ However, there are no common factors between $21g(2g - 1)$ and $(g + 1)(3g + 5)$ , so the expression is already in its simplest form.
Final Answer: The final answer is the expression we have after the multiplication, which is $(21g(2g - 1))/((g + 1)(3g + 5))$ .