Simplify (5 square root of c+2)/(3+ square root of c)

Math
5c+23+c
Multiply 5c+23+c by 3-c3-c.
5c+23+c⋅3-c3-c
Combine fractions.
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Multiply 5c+23+c and 3-c3-c.
(5c+2)(3-c)(3+c)(3-c)
Expand the denominator using the FOIL method.
(5c+2)(3-c)9-3c+c⋅3-c2
Simplify.
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Use axn=axn to rewrite c as c12.
(5c+2)(3-c)9-(c12)2
Apply the power rule and multiply exponents, (am)n=amn.
(5c+2)(3-c)9-c12⋅2
Combine 12 and 2.
(5c+2)(3-c)9-c22
Cancel the common factor of 2.
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Cancel the common factor.
(5c+2)(3-c)9-c22
Divide 1 by 1.
(5c+2)(3-c)9-c1
(5c+2)(3-c)9-c1
Simplify.
(5c+2)(3-c)9-c
(5c+2)(3-c)9-c
(5c+2)(3-c)9-c
Expand (5c+2)(3-c) using the FOIL Method.
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Apply the distributive property.
5c(3-c)+2(3-c)9-c
Apply the distributive property.
5c⋅3+5c(-c)+2(3-c)9-c
Apply the distributive property.
5c⋅3+5c(-c)+2⋅3+2(-c)9-c
5c⋅3+5c(-c)+2⋅3+2(-c)9-c
Simplify and combine like terms.
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Simplify each term.
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Multiply 3 by 5.
15c+5c(-c)+2⋅3+2(-c)9-c
Multiply 5c(-c).
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Multiply -1 by 5.
15c-5cc+2⋅3+2(-c)9-c
Raise c to the power of 1.
15c-5(c1c)+2⋅3+2(-c)9-c
Raise c to the power of 1.
15c-5(c1c1)+2⋅3+2(-c)9-c
Use the power rule aman=am+n to combine exponents.
15c-5c1+1+2⋅3+2(-c)9-c
Add 1 and 1.
15c-5c2+2⋅3+2(-c)9-c
15c-5c2+2⋅3+2(-c)9-c
Rewrite c2 as c.
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Use axn=axn to rewrite c as c12.
15c-5(c12)2+2⋅3+2(-c)9-c
Apply the power rule and multiply exponents, (am)n=amn.
15c-5c12⋅2+2⋅3+2(-c)9-c
Combine 12 and 2.
15c-5c22+2⋅3+2(-c)9-c
Cancel the common factor of 2.
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Cancel the common factor.
15c-5c22+2⋅3+2(-c)9-c
Divide 1 by 1.
15c-5c1+2⋅3+2(-c)9-c
15c-5c1+2⋅3+2(-c)9-c
Simplify.
15c-5c+2⋅3+2(-c)9-c
15c-5c+2⋅3+2(-c)9-c
Multiply 2 by 3.
15c-5c+6+2(-c)9-c
Multiply -1 by 2.
15c-5c+6-2c9-c
15c-5c+6-2c9-c
Subtract 2c from 15c.
-5c+6+13c9-c
-5c+6+13c9-c
Factor -1 out of -5c.
-(5c)+6+13c9-c
Rewrite 6 as -1(-6).
-(5c)-1(-6)+13c9-c
Factor -1 out of -(5c)-1(-6).
-(5c-6)+13c9-c
Factor -1 out of 13c.
-(5c-6)-(-13c)9-c
Factor -1 out of -(5c-6)-(-13c).
-(5c-6-13c)9-c
Simplify the expression.
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Rewrite -(5c-6-13c) as -1(5c-6-13c).
-1(5c-6-13c)9-c
Move the negative in front of the fraction.
-5c-6-13c9-c
-5c-6-13c9-c
Simplify (5 square root of c+2)/(3+ square root of c)

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