Question

what is the quotient?
\frac{a - 3}{7} \div \frac{3 - a}{21}
options:
\frac{(a - 3)^2}{147}
3
-3
\frac{-(a - 3)^2}{147}

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, multiply by its reciprocal. So, \(\frac{a - 3}{7}\div\frac{3 - a}{21}=\frac{a - 3}{7}\times\frac{21}{3 - a}\)

Step2: Simplify the expression

Notice that \(3 - a=-(a - 3)\). Substitute this into the expression: \(\frac{a - 3}{7}\times\frac{21}{-(a - 3)}\)
Cancel out the common factor \((a - 3)\) (assuming \(a
eq3\)): \(\frac{1}{7}\times\frac{21}{- 1}\)
Simplify \(\frac{21}{7}=3\), so we have \(3\times(- 1)=-3\)

Answer:

\(-3\)