Simplify ((n-9)/n)÷((n^2-81)/(7n^2))

Math
n-9n÷n2-817n2
To divide by a fraction, multiply by its reciprocal.
n-9n⋅7n2n2-81
Cancel the common factor of n.
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Factor n out of 7n2.
n-9n⋅n(7n)n2-81
Cancel the common factor.
n-9n⋅n(7n)n2-81
Rewrite the expression.
(n-9)7nn2-81
(n-9)7nn2-81
Simplify the denominator.
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Rewrite 81 as 92.
(n-9)7nn2-92
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=n and b=9.
(n-9)7n(n+9)(n-9)
(n-9)7n(n+9)(n-9)
Cancel the common factor of n-9.
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Factor n-9 out of (n+9)(n-9).
(n-9)7n(n-9)(n+9)
Cancel the common factor.
(n-9)7n(n-9)(n+9)
Rewrite the expression.
7nn+9
7nn+9
Simplify ((n-9)/n)÷((n^2-81)/(7n^2))

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