# Simplify 6/(n-3)+n/(n+3)

6n-3+nn+3
To write 6n-3 as a fraction with a common denominator, multiply by n+3n+3.
6n-3⋅n+3n+3+nn+3
To write nn+3 as a fraction with a common denominator, multiply by n-3n-3.
6n-3⋅n+3n+3+nn+3⋅n-3n-3
Write each expression with a common denominator of (n-3)(n+3), by multiplying each by an appropriate factor of 1.
Multiply 6n-3 and n+3n+3.
6(n+3)(n-3)(n+3)+nn+3⋅n-3n-3
Multiply nn+3 and n-3n-3.
6(n+3)(n-3)(n+3)+n(n-3)(n+3)(n-3)
Reorder the factors of (n-3)(n+3).
6(n+3)(n+3)(n-3)+n(n-3)(n+3)(n-3)
6(n+3)(n+3)(n-3)+n(n-3)(n+3)(n-3)
Combine the numerators over the common denominator.
6(n+3)+n(n-3)(n+3)(n-3)
Simplify the numerator.
Apply the distributive property.
6n+6⋅3+n(n-3)(n+3)(n-3)
Multiply 6 by 3.
6n+18+n(n-3)(n+3)(n-3)
Apply the distributive property.
6n+18+n⋅n+n⋅-3(n+3)(n-3)
Multiply n by n.
6n+18+n2+n⋅-3(n+3)(n-3)
Move -3 to the left of n.
6n+18+n2-3⋅n(n+3)(n-3)
Subtract 3n from 6n.
3n+18+n2(n+3)(n-3)
Reorder terms.
n2+3n+18(n+3)(n-3)
n2+3n+18(n+3)(n-3)
Simplify 6/(n-3)+n/(n+3)