Multiply
16-n^2 n^2-7n-30
_________ __________
n^2-5n-36 * n^2-n-12
again, I think you mean:
(16-n^2)/(n^2 - 5n - 36) * (n^2 - 7n - 30)/(n^2 - n - 12)
= (4-n)(4+n)/( (n-9)(n+4)) * (n-10)(n+3)/( (n-4)(n+3) )
= (n-10)/(n-9) , n ≠ ±4, -3
Divide
x^3y^2(x^2-3x-18)/xy^5(x^2-x-30)
To multiply the given expressions, follow these steps:
Step 1: Factorize the denominators
Factorize the denominators of both fractions:
n^2-5n-36 can be factored as (n-9)(n+4)
n^2-n-12 can be factored as (n-4)(n+3)
So the expression becomes:
[(16-n^2)/(n-9)(n+4)] * [(n^2-7n-30)/(n-4)(n+3)]
Step 2: Simplify the numerators
In the first fraction, the numerator is 16-n^2, which is already simplified.
In the second fraction, the numerator is n^2-7n-30, which can be factored as (n-10)(n+3).
So the expression becomes:
[(16-n^2)/(n-9)(n+4)] * [((n-10)(n+3))/(n-4)(n+3)]
Step 3: Simplify further
Now, we can simplify the expression. Observe that (n+3) is present in both the numerator and denominator of the second fraction. These terms can cancel each other out.
[(16-n^2)/(n-9)(n+4)] * [(n-10)/(n-4)]
Step 4: Multiply the numerators and denominators
To multiply the fractions, simply multiply the numerators together and the denominators together:
[(16-n^2) * (n-10)] / [(n-9)(n+4)(n-4)]
Step 5: Simplify the numerator and denominator
Expand and simplify the numerator:
(16n - 160 - n^3 + 10n^2) / [(n-9)(n+4)(n-4)]
Step 6: Rearrange the terms
Rearrange the terms in descending order of the degree of n:
(-n^3 + 10n^2 + 16n - 160) / [(n-9)(n-4)(n+4)]
And that's the final answer, given as a simplified expression.