Divide (2a+6)÷((a^2-9)/(2a))

Math
(2a+6)÷a2-92a
To divide by a fraction, multiply by its reciprocal.
(2a+6)2aa2-9
Simplify the denominator.
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Rewrite 9 as 32.
(2a+6)2aa2-32
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=3.
(2a+6)2a(a+3)(a-3)
(2a+6)2a(a+3)(a-3)
Multiply 2a+6 and 2a(a+3)(a-3).
(2a+6)(2a)(a+3)(a-3)
Simplify the numerator.
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Factor 2 out of 2a+6.
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Factor 2 out of 2a.
(2(a)+6)⋅2a(a+3)(a-3)
Factor 2 out of 6.
(2a+2⋅3)⋅2a(a+3)(a-3)
Factor 2 out of 2a+2⋅3.
2(a+3)⋅2a(a+3)(a-3)
2(a+3)⋅2a(a+3)(a-3)
Multiply 2 by 2.
4(a+3)a(a+3)(a-3)
4(a+3)a(a+3)(a-3)
Cancel the common factor of a+3.
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Cancel the common factor.
4(a+3)a(a+3)(a-3)
Rewrite the expression.
4aa-3
4aa-3
Divide (2a+6)÷((a^2-9)/(2a))

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