simplify: (x-(1/x^2))/(x-(1/x^3))
simplify: 4+___d___
4+_4_
4+d
I'm not quite sure what the second question says, but for the first question you'll be needing common denominators. Working on the numerator first, we have $\displaystyle x - \frac{1}{x^2}$. To get a common denominator, multiply $\displaystyle x \cdot \frac{x^2}{x^2}$ so that you get $\displaystyle \frac{x^3}{x^2} - \frac{1}{x^2}$. Subtracting yields $\displaystyle \frac{x^3 - 1}{x^2}$. Can you simplify the denominator?
For the first question, you should have gotten $\displaystyle \frac{x^4 - 1}{x^3}$ as the denominator, which leaves you with $\displaystyle \frac{\frac{x^3 - 1}{x^2}}{\frac{x^4 - 1}{x^3}}$. Now, you can rearrange this (using the reciprocal rule) to $\displaystyle \frac{x^3(x^3 - 1)}{x^2(x^4 - 1)}$. You can cancel out x^2 in the top and bottom to yield $\displaystyle \frac{x(x^3 - 1)}{x^4 - 1}$ and then remove a factor of x-1 from both top and bottom to yield $\displaystyle \frac{x(x^2 + x + 1)}{x^3 + x^2 + x + 1}$ and that's as simplified as it gets.
For the second question, using the parentheses, work from the inside out, using common denominators to combine fractions.