Answer:
Option C is correct
the expression which is equivalent to the expression [tex]\frac{\frac{c^2-4}{c+3}}{\frac{c+2}{3(c^2-9)} }[/tex] is, [tex]\frac{c^2-4}{c+3} \cdot \frac{3(c^2-9)}{c+2}[/tex]
Explanation:
Given: The expression is: [tex]\frac{\frac{c^2-4}{c+3}}{\frac{c+2}{c^2-9} }[/tex]
We remember that dividing fraction a by fraction b is the same as multiplying fraction a by the reciprocal of fraction b or vice versa.
Using expression: [tex]\frac{\frac{p}{q}}{\frac{r}{s} }[/tex]
⇒ [tex]\frac{p}{q} \cdot \frac{s}{r}[/tex]
Let p=[tex]c^2-4[/tex], q=c+3 , r =c+2 and s = [tex]3(c^2-9)[/tex]
then;
[tex]\frac{\frac{p}{q}}{\frac{r}{s} }[/tex] = [tex]\frac{p}{q} \cdot \frac{s}{r}[/tex]
= [tex]\frac{c^2-4}{c+3} \cdot \frac{3(c^2-9)}{c+2}[/tex]
Therefore, the expression which is equivalent to the given expression is,
[tex]\frac{c^2-4}{c+3} \cdot \frac{3(c^2-9)}{c+2}[/tex]
