Question

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

Explanation:

Step1: Rewrite division as multiplication

$\frac{a-3}{7} \div \frac{3-a}{21} = \frac{a-3}{7} \times \frac{21}{3-a}$

Step2: Factor out -1 from denominator

Note that $3-a = -(a-3)$, so substitute:
$\frac{a-3}{7} \times \frac{21}{-(a-3)}$

Step3: Simplify the expression

Cancel $(a-3)$ terms, then simplify $\frac{21}{7}$:
$\frac{21}{7 \times (-1)} = \frac{3}{-1}$

Answer:

-3