Question

Please help! I attached the question below.

Answer 1

Answer:

$\frac{2(c+2)}{c(c-2)}$

Step-by-step explanation:

$\frac{c^{2}-4 }{6c^{4}+15c^{3}}=\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2}) }$

Identity used:

$a^{2}-b^{2}=(a-b)(a+b)$

$\frac{c^{2}-4c+4}{12c^{3}+30c^{2}}=\frac{(c-2)^{2}}{2(6c^{3}+15c^{2}) }$

Now let us divide the modified expressions:

$\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2})}$ ÷ $\frac{(c-2)^2}{2(6c^{3}+15c^{2}) }$

we get:

$\frac{2(c+2)}{c(c-2)}$