Divide. Write your answer in simplest form. $$ \frac{4 k-8}{7 k} \div(2 k+1) $$

Question

UpStudy AI · Accepted Answer

1. Begin with the expression:

$$
   \frac{4k-8}{7k} \div (2k+1)
   $$

2. Dividing by a number is equivalent to multiplying by its reciprocal. Thus, rewrite the expression as:

$$
   \frac{4k-8}{7k} \cdot \frac{1}{2k+1}
   $$

3. Factor the numerator $$4k-8$$:

$$
   4k-8 = 4(k-2)
   $$

4. Substitute back into the expression:

$$
   \frac{4(k-2)}{7k} \cdot \frac{1}{2k+1} = \frac{4(k-2)}{7k(2k+1)}
   $$

5. The final answer in simplest form is:

$$
   \frac{4(k-2)}{7k(2k+1)}
   $$
The simplified form of the expression is $$ \frac{4(k-2)}{7k(2k+1)} $$.

Divide. Write your answer in simplest form. \[ \frac{4 k-8}{7 k} \div(2 k+1) \]