# Simplify ((3(a+2))/(a^2-1))÷((a^2-4)/(2a^2+2a))

3(a+2)a2-1÷a2-42a2+2a
To divide by a fraction, multiply by its reciprocal.
3(a+2)a2-1⋅2a2+2aa2-4
Simplify the denominator.
Rewrite 1 as 12.
3(a+2)a2-12⋅2a2+2aa2-4
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=1.
3(a+2)(a+1)(a-1)⋅2a2+2aa2-4
3(a+2)(a+1)(a-1)⋅2a2+2aa2-4
Factor 2a out of 2a2+2a.
Factor 2a out of 2a2.
3(a+2)(a+1)(a-1)⋅2a(a)+2aa2-4
Factor 2a out of 2a.
3(a+2)(a+1)(a-1)⋅2a(a)+2a(1)a2-4
Factor 2a out of 2a(a)+2a(1).
3(a+2)(a+1)(a-1)⋅2a(a+1)a2-4
3(a+2)(a+1)(a-1)⋅2a(a+1)a2-4
Simplify the denominator.
Rewrite 4 as 22.
3(a+2)(a+1)(a-1)⋅2a(a+1)a2-22
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=2.
3(a+2)(a+1)(a-1)⋅2a(a+1)(a+2)(a-2)
3(a+2)(a+1)(a-1)⋅2a(a+1)(a+2)(a-2)
Simplify terms.
Cancel the common factor of a+2.
Factor a+2 out of 3(a+2).
(a+2)⋅3(a+1)(a-1)⋅2a(a+1)(a+2)(a-2)
Cancel the common factor.
(a+2)⋅3(a+1)(a-1)⋅2a(a+1)(a+2)(a-2)
Rewrite the expression.
3(a+1)(a-1)⋅2a(a+1)a-2
3(a+1)(a-1)⋅2a(a+1)a-2
Cancel the common factor of a+1.
Factor a+1 out of 2a(a+1).
3(a+1)(a-1)⋅(a+1)(2a)a-2
Cancel the common factor.
3(a+1)(a-1)⋅(a+1)(2a)a-2
Rewrite the expression.
3a-1⋅2aa-2
3a-1⋅2aa-2
Multiply 3a-1 and 2aa-2.
3(2a)(a-1)(a-2)
Multiply 2 by 3.
6a(a-1)(a-2)
6a(a-1)(a-2)
Simplify ((3(a+2))/(a^2-1))÷((a^2-4)/(2a^2+2a))

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