What is the value of $\left(\frac{x^{2}-x-6}{x^{2}+x-12}\right) \div \left(\frac{x^{2}+5x+6}{x^{2}+7x+12}\right)?$

If $a+b+c=0,$ then the value of $\left(\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}\right)$ is:

Let $f(x) = a_{0}x^{n} + a_{1}x^{n-1} + a_{2}x^{n-2} + \ldots + a_{n-1}x + a_{n}$,where $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$ are constants. If $f(x)$ is divided by $ax - b$,then the remainder is:

If $x+y+z=9$ and $xy+yz+zx=23$,then the value of $x^3+y^3+z^3-3xyz$ is

If $2 a p q = (p + q)^2 - (p - q)^2$,then the value of $a$ is

Find the factors of $(a-b)^{3}+(b-c)^{3}+(c-a)^{3}$.