hi i made a typo in my last question can u please show me step by step how to simplify

[(x^3/y^3) -1]/[(x^2/y^2)+(x/y)+1]

Certainly! Let's simplify the expression step by step.

Step 1: Simplify the numerator.
In the numerator, we have (x^3/y^3) - 1. To simplify this, we need a common denominator for the terms. The common denominator will be y^3.

So, (x^3/y^3) - 1 becomes (x^3 - y^3)/y^3.

Step 2: Simplify the denominator.
In the denominator, we have (x^2/y^2) + (x/y) + 1. To simplify this, we need a common denominator for all three terms. The common denominator will be y^2.

So, (x^2/y^2) + (x/y) + 1 becomes (x^2y/y^2) + (xy^2/y^2) + y^2/y^2.

Simplifying further, we have:
(x^2y + xy^2 + y^2)/y^2.

Step 3: Rewrite the expression.
Now that we have simplified the numerator and the denominator, we can rewrite the expression as:
(x^3 - y^3)/y^3 divided by (x^2y + xy^2 + y^2)/y^2.

Step 4: Simplify the fraction by multiplying by the reciprocal.
To divide by a fraction, we can multiply by its reciprocal. So we will multiply by the reciprocal of the denominator to simplify further.

The reciprocal of (x^2y + xy^2 + y^2)/y^2 is y^2/(x^2y + xy^2 + y^2).

Multiplying the numerator by y^2 and the denominator by (x^2y + xy^2 + y^2), we get:
[(x^3 - y^3)/y^3] * [y^2/(x^2y + xy^2 + y^2)].

Step 5: Simplify the expression.
Finally, let's simplify the expression further. In the numerator, the y^3 cancels out with one of the y^2 terms in the denominator.

[(x^3 - y^3)/y^2] * [y^2/(x^2y + xy^2 + y^2)]
= (x^3 - y^3)/(x^2y + xy^2 + y^2).

And that's the simplified expression: (x^3 - y^3)/(x^2y + xy^2 + y^2).