Simplify ((a+b)/(ab))/((a^2-b^2)/(2a^4b))

Math
a+baba2-b22a4b
Multiply the numerator by the reciprocal of the denominator.
a+bab⋅2a4ba2-b2
Cancel the common factor of ab.
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Factor ab out of 2a4b.
a+bab⋅ab(2a3)a2-b2
Cancel the common factor.
a+bab⋅ab(2a3)a2-b2
Rewrite the expression.
(a+b)2a3a2-b2
(a+b)2a3a2-b2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=b.
(a+b)2a3(a+b)(a-b)
Cancel the common factor of a+b.
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Cancel the common factor.
(a+b)2a3(a+b)(a-b)
Rewrite the expression.
2a3a-b
2a3a-b
Simplify ((a+b)/(ab))/((a^2-b^2)/(2a^4b))

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