# Simplify (5 square root of S)/(2 square root of S+ square root of 4) 5S2S+4
Simplify the denominator.
Rewrite 4 as 22.
5S2S+22
Pull terms out from under the radical, assuming positive real numbers.
5S2S+2
Factor 2 out of 2S+2.
Factor 2 out of 2S.
5S2(S)+2
Factor 2 out of 2.
5S2(S)+2(1)
Factor 2 out of 2(S)+2(1).
5S2(S+1)
5S2(S+1)
5S2(S+1)
Multiply 5S2(S+1) by S-1S-1.
5S2(S+1)⋅S-1S-1
Multiply 5S2(S+1) and S-1S-1.
5S(S-1)2(S+1)(S-1)
Reorder.
Move S+1.
5S(S-1)2((S+1)(S-1))
Expand the denominator using the FOIL method.
5S(S-1)2(S2+S⋅-1+S-1)
Simplify.
Use axn=axn to rewrite S as S12.
5S(S-1)2((S12)2-1)
Apply the power rule and multiply exponents, (am)n=amn.
5S(S-1)2(S12⋅2-1)
Combine 12 and 2.
5S(S-1)2(S22-1)
Cancel the common factor of 2.
Cancel the common factor.
5S(S-1)2(S22-1)
Divide 1 by 1.
5S(S-1)2(S1-1)
5S(S-1)2(S1-1)
Simplify.
5S(S-1)2(S-1)
5S(S-1)2(S-1)
Group S-1 and S together.
5((S-1)S)2(S-1)
5((S-1)S)2(S-1)
Apply the distributive property.
5(SS-1S)2(S-1)
Multiply SS.
Raise S to the power of 1.
5(S1S-1S)2(S-1)
Raise S to the power of 1.
5(S1S1-1S)2(S-1)
Use the power rule aman=am+n to combine exponents.
5(S1+1-1S)2(S-1)
5(S2-1S)2(S-1)
5(S2-1S)2(S-1)
Rewrite -1S as -S.
5(S2-S)2(S-1)
Rewrite S2 as S.
Use axn=axn to rewrite S as S12.
5((S12)2-S)2(S-1)
Apply the power rule and multiply exponents, (am)n=amn.
5(S12⋅2-S)2(S-1)
Combine 12 and 2.
5(S22-S)2(S-1)
Cancel the common factor of 2.
Cancel the common factor.
5(S22-S)2(S-1)
Divide 1 by 1.
5(S1-S)2(S-1)
5(S1-S)2(S-1)
Simplify.
5(S-S)2(S-1)
5(S-S)2(S-1)
Simplify (5 square root of S)/(2 square root of S+ square root of 4)

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