Divide ((z^2-9)/z)÷((z+3)/(z-3))

Math
z2-9z÷z+3z-3
To divide by a fraction, multiply by its reciprocal.
z2-9z⋅z-3z+3
Simplify the numerator.
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Rewrite 9 as 32.
z2-32z⋅z-3z+3
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=z and b=3.
(z+3)(z-3)z⋅z-3z+3
(z+3)(z-3)z⋅z-3z+3
Cancel the common factor of z+3.
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Cancel the common factor.
(z+3)(z-3)z⋅z-3z+3
Rewrite the expression.
z-3z(z-3)
z-3z(z-3)
Multiply z-3z and z-3.
(z-3)(z-3)z
Simplify the numerator.
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Raise z-3 to the power of 1.
(z-3)1(z-3)z
Raise z-3 to the power of 1.
(z-3)1(z-3)1z
Use the power rule aman=am+n to combine exponents.
(z-3)1+1z
Add 1 and 1.
(z-3)2z
(z-3)2z
Rewrite (z-3)2 as (z-3)(z-3).
(z-3)(z-3)z
Expand (z-3)(z-3) using the FOIL Method.
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Apply the distributive property.
z(z-3)-3(z-3)z
Apply the distributive property.
z⋅z+z⋅-3-3(z-3)z
Apply the distributive property.
z⋅z+z⋅-3-3z-3⋅-3z
z⋅z+z⋅-3-3z-3⋅-3z
Simplify and combine like terms.
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Simplify each term.
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Multiply z by z.
z2+z⋅-3-3z-3⋅-3z
Move -3 to the left of z.
z2-3⋅z-3z-3⋅-3z
Multiply -3 by -3.
z2-3z-3z+9z
z2-3z-3z+9z
Subtract 3z from -3z.
z2-6z+9z
z2-6z+9z
Split the fraction z2-6z+9z into two fractions.
z2-6zz+9z
Split the fraction z2-6zz into two fractions.
z2z+-6zz+9z
Cancel the common factor of z2 and z.
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Factor z out of z2.
z⋅zz+-6zz+9z
Cancel the common factors.
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Raise z to the power of 1.
z⋅zz1+-6zz+9z
Factor z out of z1.
z⋅zz⋅1+-6zz+9z
Cancel the common factor.
z⋅zz⋅1+-6zz+9z
Rewrite the expression.
z1+-6zz+9z
Divide z by 1.
z+-6zz+9z
z+-6zz+9z
z+-6zz+9z
Cancel the common factor of z.
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Cancel the common factor.
z+-6zz+9z
Divide -6 by 1.
z-6+9z
z-6+9z
Divide ((z^2-9)/z)÷((z+3)/(z-3))

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