Question

Divide. Express the quotient in simplest form.
x^2−x−12/2x^2÷x^2+x−6/2x^3

Answer 1

Hey there!

These are technically expressed as fraction. When you divide a fraction by another, you can replace the second fraction with its reciprocal and you can now multiply the fractions together instead. 

$\frac{x^2-x-12}{2x^2} / \frac{x^2+x-6}{2x^3}$

$\frac{x^2-x-12}{2x^2} * \frac{2x^3}{x^2+x-6}$

Now, just multiply across the top and the bottom. You can first cancel out any terms that are repeated or similar. 

$\frac{12}{2x^2} * \frac{2x^3}{-6}$

$\frac{2}{x} * \frac{1}{-1}$

$\frac{2}{-x}$

Your answer will be $\frac{2}{-x}$. 

Hope this helped you out! :-)

Answer 2

I strongly urge you to use parentheses here, to remove any ambiguity regarding which quantity is being divided by which quantity.  I'm assuming that you meant

(x^2−x−12)/(2x^2)÷(x^2+x−6)/2x^3.  If that is correct, great.  If not, fix it!  Once correct, you can perform the divisions from left to right, beginning with (x^2-x-12)/2x^2.