How do you simplify this equation? I saw it in a workbook and I can't figure out how you can simplify it because of the subtraction operation.

$$\left( a - a^{-3} \right) \div \left( a^{-3} - 1 \right)$$

Question

How do you simplify this equation? I saw it in a workbook and I can't figure out how you can simplify it because of the subtraction operation. 

$$\left( a - a^{-3} \right) \div \left( a^{-3} - 1 \right)$$

anonymous · Answer

youwrite it as a fraction then you flip the negative powers

anonymous · Answer

$$(a-1/a ^{3})/(1/a ^{3} -1)$$

anonymous · Answer

sorry west thats wrong

anonymous · Answer

he didnt even do anything but invert the exponents lol

anonymous · Answer

yea i think just flip the -exponets then you are done

anonymous · Answer

Then, you can easily carry out the basic operations and you get the following:
$$-a ^{3}-1$$

anonymous · Answer

$$\frac{a^4-1}{1-a^3}=\frac{(a-1)(a+1)(a^2+1)}{(1-a)(1+a+a^2)}$$

anonymous · Answer

Huh. What puzzled me was that the workbook was multiple choice and the choices were stuff like just [ a ] and [ 1/a ]. 

Could be that I'm recalling the actual equation incorrectly since it was some time ago, but the basic premise is the same. 

I think I get what Aron is saying now. Cross multiplication, right? 
NotSObright's answer is also a neat trick that I keep forgetting when simplifying. 

Thanks guys!