Multiply (2n-3)/(n+1)*(2n^2+5n+3)/(9-4n^2)

Math
2n-3n+1⋅2n2+5n+39-4n2
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅3=6 and whose sum is b=5.
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Factor 5 out of 5n.
2n-3n+1⋅2n2+5(n)+39-4n2
Rewrite 5 as 2 plus 3
2n-3n+1⋅2n2+(2+3)n+39-4n2
Apply the distributive property.
2n-3n+1⋅2n2+2n+3n+39-4n2
2n-3n+1⋅2n2+2n+3n+39-4n2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
2n-3n+1⋅(2n2+2n)+3n+39-4n2
Factor out the greatest common factor (GCF) from each group.
2n-3n+1⋅2n(n+1)+3(n+1)9-4n2
2n-3n+1⋅2n(n+1)+3(n+1)9-4n2
Factor the polynomial by factoring out the greatest common factor, n+1.
2n-3n+1⋅(n+1)(2n+3)9-4n2
2n-3n+1⋅(n+1)(2n+3)9-4n2
Simplify the denominator.
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Rewrite 9 as 32.
2n-3n+1⋅(n+1)(2n+3)32-4n2
Rewrite 4n2 as (2n)2.
2n-3n+1⋅(n+1)(2n+3)32-(2n)2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=3 and b=2n.
2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-(2n))
Multiply 2 by -1.
2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-2n)
2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-2n)
Simplify terms.
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Cancel the common factor of n+1.
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Cancel the common factor.
2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-2n)
Rewrite the expression.
(2n-3)⋅2n+3(3+2n)(3-2n)
(2n-3)⋅2n+3(3+2n)(3-2n)
Cancel the common factor of 2n+3 and 3+2n.
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Reorder terms.
(2n-3)⋅2n+3(2n+3)(3-2n)
Cancel the common factor.
(2n-3)⋅2n+3(2n+3)(3-2n)
Rewrite the expression.
(2n-3)⋅13-2n
(2n-3)⋅13-2n
Multiply 2n-3 and 13-2n.
2n-33-2n
Cancel the common factor of 2n-3 and 3-2n.
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Factor -1 out of 2n.
-(-2n)-33-2n
Rewrite -3 as -1(3).
-(-2n)-1(3)3-2n
Factor -1 out of -(-2n)-1(3).
-(-2n+3)3-2n
Rewrite -(-2n+3) as -1(-2n+3).
-1(-2n+3)3-2n
Reorder terms.
-1(-2n+3)-2n+3
Cancel the common factor.
-1(-2n+3)-2n+3
Divide -1 by 1.
-1
-1
-1
Multiply (2n-3)/(n+1)*(2n^2+5n+3)/(9-4n^2)

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