Answer:
[tex]\frac{2(c+2)}{c(c-2)}[/tex]
Step-by-step explanation:
[tex]\frac{c^{2}-4 }{6c^{4}+15c^{3}}=\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2}) }[/tex]
Identity used:
[tex]a^{2}-b^{2}=(a-b)(a+b)[/tex]
[tex]\frac{c^{2}-4c+4}{12c^{3}+30c^{2}}=\frac{(c-2)^{2}}{2(6c^{3}+15c^{2}) }[/tex]
Now let us divide the modified expressions:
[tex]\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2})}[/tex] ÷ [tex]\frac{(c-2)^2}{2(6c^{3}+15c^{2}) }[/tex]
we get:
[tex]\frac{2(c+2)}{c(c-2)}[/tex]
