Answer :
Answer:
C
Step-by-step explanation:
Given:
[tex]\dfrac{c^2-4}{c+3}\div \dfrac{c+2}{3(c^2-9)}[/tex]
Changing the division to multiplication by taking the reciprocal of the second fraction.
[tex]\dfrac{c^2-4}{c+3}X \dfrac{3(c^2-9)}{c+2}[/tex]
The correct option is C
The expression that is equivalent to the given function is (c - 2)(3c-9)
Given the expression:
- [tex]\frac{c^2-4}{c+3}\div\frac{c+2}{3(c^2-9)}[/tex]
According to the difference of two squares;
- [tex]a^2 - b^2 = (a-b)(a+b)[/tex]
Applying this to the equation will result into;
[tex]= \frac{c^2-2^2}{c+3}\div \frac{c+2}{3(c^2-3^2)}\\ =\frac{(c+2)(c-2)}{c+3}\div \frac{c+2}{3(c+3)(c-3)}\\ =\frac{(c+2)(c-2)}{c+3} \times \frac{3(c-3)(c+3)}{c+2}\\[/tex]
Cancel out the common terms from both numerator and denominator;
[tex]=\frac{(c+2)(c-2)}{c+3} \times \frac{3(c-3)(c+3)}{c+2}\\=c-2 \times 3(c-3)\\=(c-2)(3c-9)\\[/tex]
Hence the expression that is equivalent to the given function is (c - 2)(3c-9)
Learn more on difference of functions here: https://brainly.com/question/17431959