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).