Question

How do you simplify `(2/x^3 + y)/(x - 1/y^2)`?

Answer 1

We can rewrite the expression `(2/x^3+y)/(x-1/y^2)` as `(2x^-3+y)/(x-y^-2)` and then use the properties of indices to simplify the `x` and `y` terms separately, yielding `2x^-4-y^3`.

Explanation:

It might just be a quirk of mine, but when simplifying things I like to try to deal with fractions first.

By using negative indices, the original expression `(2/x^3+y)/(x-1/y^2)` can be converted to `(2x^-3+y)/(x-y^-2)`.

Now we can treat the `x` and `y` terms separately:

`(2x^-3)/(x) = 2x^-4` (since we divided by `x`)

`(y)/(-y^-2) = -y^3` (since we divided by `-y^2`)

Putting it all together:

`(2/x^3+y)/(x-1/y^2)` = `2x^-4-y^3`.