# Simplify (s^2-16)/(9s+36)*(27s+108)/(3s^2-24s+48)

s2-169s+36⋅27s+1083s2-24s+48
Simplify the numerator.
Rewrite 16 as 42.
s2-429s+36⋅27s+1083s2-24s+48
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=s and b=4.
(s+4)(s-4)9s+36⋅27s+1083s2-24s+48
(s+4)(s-4)9s+36⋅27s+1083s2-24s+48
Simplify with factoring out.
Factor 9 out of 9s+36.
Factor 9 out of 9s.
(s+4)(s-4)9(s)+36⋅27s+1083s2-24s+48
Factor 9 out of 36.
(s+4)(s-4)9s+9⋅4⋅27s+1083s2-24s+48
Factor 9 out of 9s+9⋅4.
(s+4)(s-4)9(s+4)⋅27s+1083s2-24s+48
(s+4)(s-4)9(s+4)⋅27s+1083s2-24s+48
Factor 27 out of 27s+108.
Factor 27 out of 27s.
(s+4)(s-4)9(s+4)⋅27(s)+1083s2-24s+48
Factor 27 out of 108.
(s+4)(s-4)9(s+4)⋅27s+27⋅43s2-24s+48
Factor 27 out of 27s+27⋅4.
(s+4)(s-4)9(s+4)⋅27(s+4)3s2-24s+48
(s+4)(s-4)9(s+4)⋅27(s+4)3s2-24s+48
(s+4)(s-4)9(s+4)⋅27(s+4)3s2-24s+48
Simplify the denominator.
Factor 3 out of 3s2-24s+48.
Factor 3 out of 3s2.
(s+4)(s-4)9(s+4)⋅27(s+4)3(s2)-24s+48
Factor 3 out of -24s.
(s+4)(s-4)9(s+4)⋅27(s+4)3(s2)+3(-8s)+48
Factor 3 out of 48.
(s+4)(s-4)9(s+4)⋅27(s+4)3s2+3(-8s)+3⋅16
Factor 3 out of 3s2+3(-8s).
(s+4)(s-4)9(s+4)⋅27(s+4)3(s2-8s)+3⋅16
Factor 3 out of 3(s2-8s)+3⋅16.
(s+4)(s-4)9(s+4)⋅27(s+4)3(s2-8s+16)
(s+4)(s-4)9(s+4)⋅27(s+4)3(s2-8s+16)
Factor using the perfect square rule.
Rewrite 16 as 42.
(s+4)(s-4)9(s+4)⋅27(s+4)3(s2-8s+42)
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅s⋅-4
Simplify.
2ab=-8s
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=s and b=-4.
(s+4)(s-4)9(s+4)⋅27(s+4)3(s-4)2
(s+4)(s-4)9(s+4)⋅27(s+4)3(s-4)2
(s+4)(s-4)9(s+4)⋅27(s+4)3(s-4)2
Simplify terms.
Cancel the common factor of s-4.
Factor s-4 out of (s+4)(s-4).
(s-4)(s+4)9(s+4)⋅27(s+4)3(s-4)2
Factor s-4 out of 3(s-4)2.
(s-4)(s+4)9(s+4)⋅27(s+4)(s-4)(3(s-4))
Cancel the common factor.
(s-4)(s+4)9(s+4)⋅27(s+4)(s-4)(3(s-4))
Rewrite the expression.
s+49(s+4)⋅27(s+4)3(s-4)
s+49(s+4)⋅27(s+4)3(s-4)
Cancel the common factor of 9(s+4).
Factor 9(s+4) out of 27(s+4).
s+49(s+4)⋅9(s+4)(3)3(s-4)
Cancel the common factor.
s+49(s+4)⋅9(s+4)⋅33(s-4)
Rewrite the expression.
(s+4)⋅33(s-4)
(s+4)⋅33(s-4)
Cancel the common factor of 3.
Cancel the common factor.
(s+4)⋅33(s-4)
Rewrite the expression.
(s+4)⋅1s-4
(s+4)⋅1s-4
Multiply s+4 and 1s-4.
s+4s-4
s+4s-4
Simplify (s^2-16)/(9s+36)*(27s+108)/(3s^2-24s+48)

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