Multiply or divide. Show your work.
(3n^2 -n )/(n^-1)÷(n^2)/(n+1).
(3n^2-n)/(n^-1) = n(3n-1) * n^1 = n^2(3n-1)
n^2(3n-1)÷(n^2)/(n+1)
= n^2(3n-1) * (n+1)/n^2
= (3n-1)(n+1)
thankyou
To multiply or divide the given expression, let's simplify step-by-step using the rules of exponents and the properties of fractions. Here's the step-by-step solution:
1. Simplify each expression separately:
- Simplify (3n^2 - n)/(n^-1):
To simplify the numerator, we need to combine like terms. In this case, there are no like terms, so the numerator remains as is: (3n^2 - n).
To simplify the denominator, we can apply the negative exponent rule, which states that n^-1 is equal to 1/n. Therefore, the denominator becomes 1/n.
- Simplify the denominator expression (n^2)/(n+1):
There are no further simplifications we can apply to this expression.
2. Divide the first expression by the second expression:
Division is equivalent to multiplying by the reciprocal, so we can rewrite the division as multiplication by the reciprocal of the second expression.
(3n^2 - n)/(n^-1) ÷ (n^2)/(n+1) can be rewritten as (3n^2 - n)/(n^-1) * (n+1)/(n^2).
3. Apply multiplication of fractions:
When multiplying fractions, multiply the numerators together and the denominators together.
The numerator becomes (3n^2 - n)(n + 1).
The denominator becomes (n^-1)(n^2).
4. Simplify the numerator and denominator:
Expand the numerator by multiplying the terms:
(3n^2 - n)(n + 1) = 3n^3 + 3n^2 - n^2 - n
Now multiply the denominator:
(n^-1)(n^2) = n(1/n)(n^2) = n*n^2/n = n^3
5. Combine like terms in the numerator:
Simplify the numerator further:
3n^3 + 3n^2 - n^2 - n = 3n^3 + 2n^2 - n
6. Final expression:
After simplifying the numerator and the denominator, the final expression is (3n^3 + 2n^2 - n)/(n^3).
Therefore, the answer to the expression is (3n^3 + 2n^2 - n)/(n^3).