# Simplify ( square root of r)/(3- square root of r) r3-r
Multiply r3-r by 3+r3+r.
r3-r⋅3+r3+r
Multiply r3-r and 3+r3+r.
r(3+r)(3-r)(3+r)
Expand the denominator using the FOIL method.
r(3+r)9+3r-3r-r2
Simplify.
Use axn=axn to rewrite r as r12.
r(3+r)9-(r12)2
Apply the power rule and multiply exponents, (am)n=amn.
r(3+r)9-r12⋅2
Combine 12 and 2.
r(3+r)9-r22
Cancel the common factor of 2.
Cancel the common factor.
r(3+r)9-r22
Divide 1 by 1.
r(3+r)9-r1
r(3+r)9-r1
Simplify.
r(3+r)9-r
r(3+r)9-r
Apply the distributive property.
r⋅3+rr9-r
Move 3 to the left of r.
3⋅r+rr9-r
Multiply rr.
Raise r to the power of 1.
3⋅r+r1r9-r
Raise r to the power of 1.
3⋅r+r1r19-r
Use the power rule aman=am+n to combine exponents.
3⋅r+r1+19-r
3⋅r+r29-r
3⋅r+r29-r
Rewrite r2 as r.
Use axn=axn to rewrite r as r12.
3r+(r12)29-r
Apply the power rule and multiply exponents, (am)n=amn.
3r+r12⋅29-r
Combine 12 and 2.
3r+r229-r
Cancel the common factor of 2.
Cancel the common factor.
3r+r229-r
Divide 1 by 1.
3r+r19-r
3r+r19-r
Simplify.
3r+r9-r
3r+r9-r
Simplify ( square root of r)/(3- square root of r)

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