5c+23+c

Multiply 5c+23+c by 3-c3-c.

5c+23+c⋅3-c3-c

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.

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.

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

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 each term.

Multiply 3 by 5.

15c+5c(-c)+2⋅3+2(-c)9-c

Multiply 5c(-c).

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.

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.

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

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)