Full solution

Q. Simplify. Write your answer using whole numbers and variables.

\newline

\frac{7k - 21}{k - 3}

Identify Terms: Identify the terms in the expression. $\newline$ The expression given is $7k - \frac{21}{k} - 3$ . We have three terms: $7k$ , $-\frac{21}{k}$ , and $-3$ .
Common Factors: Look for common factors in the terms. $\newline$ The terms $7k$ and $-\frac{21}{k}$ have a common factor of $7$ . The term $-3$ does not share this common factor.
Factor Out: Factor out the common factor from the terms that have it. $\newline$ We can factor out the $7$ from $7k$ and $-\frac{21}{k}$ . However, since the terms are separated by subtraction and division, we cannot factor across these operations. This means we cannot factor out the $7$ from the entire expression as it is written.
Combine Like Terms: Simplify the expression by combining like terms if possible. In this expression, there are no like terms to combine. Each term is unique in its variables and denominators.
Final Simplified Expression: Write the final simplified expression. $\newline$ Since there are no like terms to combine and no common factors to factor out across the entire expression, the expression is already in its simplest form. Therefore, the final simplified expression is $7k - \frac{21}{k} - 3$ .