Divide. Simplify your answer.

1. 2/n^3 / n-6/n^5

A: 2n^3/n-6?

2. 2x^2 + 8x + 6/x / 2x^2 + 2x/x^3 - x^2

A: 1

3. 8b^3c/b^2c / (4b^2 + 4b)

A: 1/2b^2

Please!

1. 2n^-4 -6n^5

2. x^2 + 11x + 2x^-2

3. 8c^2b

Where did you get your answers? What did you do to get those? I will tell you what you did wrong.

#1 I get

2n^2/(n-6)

#2
(2x^2 + 8x + 6)/x / (2x^2 + 2x)/(x^3 - x^2)

2(x+1)(x+3)/x / 2x(x+1)/x^2(x-1)
(x+3)/(x-1)

#3
8b^3c/b^2c / (4b^2 + 4b)
8b / 4b(b+1)
2/(b+1)

Next time, show your steps. You are evidently taking some wrong turns.

To simplify these expressions, you can follow these steps:

1. Division of Fractions: To divide fractions, we will multiply the numerator of the first fraction by the reciprocal of the second fraction.

For the first expression:
2/n^3 divided by n-6/n^5 is equivalent to (2/n^3) * (n^5/(n-6)).

Now, we can simplify the expression further. In the numerator, 2 times n^5 is 2n^5. In the denominator, n^3 times (n-6) is n^4 - 6n^3.

So the simplified form is 2n^5 / (n^4 - 6n^3).

For the second expression:
2x^2 + 8x + 6/x divided by 2x^2 + 2x/x^3 - x^2 is equivalent to (2x^2 + 8x + 6/x) * ((x^3 - x^2)/(2x^2 + 2x)).

Now, let's simplify the expression further. In the numerator, we have 2x^2 + 8x + 6 times (x^3 - x^2), which can be simplified to 2x^5 - 2x^4 + 8x^4 - 8x^3 + 6x^3 - 6x^2. In the denominator, we have (2x^2 + 2x) times x^3 - x^2, which can be simplified to 2x^5 - 2x^4 + 2x^4 - 2x^3.

We can cancel out like terms in the numerator and the denominator. Ultimately, the expression simplifies to 1.

For the third expression:
8b^3c/b^2c divided by (4b^2 + 4b) is equivalent to (8b^3c/b^2c) * (1/(4b^2 + 4b)).

Now, we simplify the expression further. In the numerator, 8b^3c divided by b^2c is equal to 8b. In the denominator, 4b^2 + 4b can be factored out to 4b(b + 1).

So the simplified form of the expression is 8b / (4b(b + 1)), which can be further simplified to 2 / (b + 1).