Question

Which expression is equivalent to StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction c + 2 Over 3 (c squared minus 9) EndFraction

Answer 1

The options have not been given but three correct alternatives have been presented as the solution.

Answer:

$3(c-2)(c-3)$ or$3(c^2-5c+6)$ or $3c^2 - 15c + 18$

Step-by-step explanation:

$\dfrac{c^2-4}{c+3}\div\dfrac{c+2}{3(c^2-9)}$

Applying the rule $a^2 - b^2 = (a+b)(a-b)$ to the numerator of the first term and the denominator of the second term,

$\dfrac{c^2-2^2}{c+3}\div\dfrac{c+2}{3(c^2-3^2)}$

$\dfrac{(c+2)(c-2)}{c+3}\div\dfrac{c+2}{3(c+3)(c-3)}$

By changing ÷ to ×, we invert the second term

$\dfrac{(c+2)(c-2)}{c+3}\times\dfrac{3(c+3)(c-3)}{c+2}$

$(c-2)\times3(c-3)$

$3(c-2)(c-3) = 3(c^2-5c+6) = 3c^2 - 15c + 18$

Answer 2

Answer:

The answer is C on edge