Simplify ((z^2-64)/z)÷((z+8)/(z+9))

Math
z2-64z÷z+8z+9
To divide by a fraction, multiply by its reciprocal.
z2-64z⋅z+9z+8
Simplify the numerator.
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Rewrite 64 as 82.
z2-82z⋅z+9z+8
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=z and b=8.
(z+8)(z-8)z⋅z+9z+8
(z+8)(z-8)z⋅z+9z+8
Simplify terms.
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Cancel the common factor of z+8.
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Cancel the common factor.
(z+8)(z-8)z⋅z+9z+8
Rewrite the expression.
z-8z(z+9)
z-8z(z+9)
Multiply z-8z and z+9.
(z-8)(z+9)z
(z-8)(z+9)z
Simplify ((z^2-64)/z)÷((z+8)/(z+9))

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