1. ## Rational Expressions (Division/Addition/Negative Exponents)

I'm not quite sure what the exact name for this type of problem.

[Instructions] Perform the indicated operations on the rational expressions and simplify.

I do not need the answer, but instead, a guide on how to solve the problem.
I am aware that I need to move the negative exponents on a denominator, but I'm not sure if it will go on the bottom -OR- make a fraction on the numerator and put the negative exponent(and its variable) on the denominator of the fraction on the numerator (and so on). I hope that makes sense. Can anybody enlighten me, please (Preferably, with numbers, as opposed to sentences - just like what I did. x_x)?

Once the negative exponents have been taken care of, it would be great to have the rest of the problem solved as well.

Any help is appreciated. Thank You,
Azusa.

2. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

What do you mean by perform the indicated operations? Your terms are not alike, so you can't add them, and trying to divide will make things very messy...

Do you mean you want to write this with positive powers?

3. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

To be honest, I do not know. But it is on the same section where I just pretty much simplified everything.
Didn't run into much problems until this one.
The answers are as follows (it may help):

Azusa.

4. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

That means you're probably expected to write everything with positive powers.

\displaystyle \displaystyle \begin{align*} \frac{3x^{-2} + 5y^{-3}}{2x^{-3} - 3y^{-2}} &= \frac{\frac{3}{x^2} + \frac{5}{y^3}}{\frac{2}{x^3} - \frac{3}{y^2}} \\ &= \frac{\frac{3y^3 + 5x^2}{x^2y^3}}{\frac{2y^2 - 3x^3}{x^3y^2}} \\ &= \frac{x^3y^2\left(3y^3 + 5x^2\right)}{x^2y^3\left(2y^2 - 3x^3\right)} \\ &= \frac{x\left(3y^3 + 5x^2\right)}{y\left(2y^2 - 3x^3\right)} \end{align*}

5. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

Thank You. Makes more sense now, but I have one last question..

Why did , turn into ?

I get the denominator part; you just combined them. But how about the numerator? Just cross multiply? Why did you cross multiply?

EDIT2: Also, I do not get how you went from
, to

Again, Thank You For Your Help,
Azusa.

bump.

7. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

To add fractions you need to get a common denominator.

8. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

I get it now. Thank you so much for your help!

9. ## Re: Rational Expressions (Division/Addition/Negative Exponents)

Originally Posted by Azusa
I'm not quite sure what the exact name for this type of problem.

[Instructions] Perform the indicated operations on the rational expressions and simplify.

I do not need the answer, but instead, a guide on how to solve the problem.
I am aware that I need to move the negative exponents on a denominator, but I'm not sure if it will go on the bottom -OR- make a fraction on the numerator and put the negative exponent(and its variable) on the denominator of the fraction on the numerator (and so on). I hope that makes sense. Can anybody enlighten me, please (Preferably, with numbers, as opposed to sentences - just like what I did. x_x)?

Once the negative exponents have been taken care of, it would be great to have the rest of the problem solved as well.

Any help is appreciated. Thank You,
Azusa.
The first thing I would do is multiply both numerator and denominator by $\displaystyle x^3y^3$ to get
$\displaystyle \frac{3xy^3+ 5x^3}{2y^3- 3x^3y}$