Simplify (1/(k+2))/(5/(k^2-4))

1k+25k2-4
Multiply the numerator by the reciprocal of the denominator.
1k+2⋅k2-45
Simplify the numerator.
Rewrite 4 as 22.
1k+2⋅k2-225
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=k and b=2.
1k+2⋅(k+2)(k-2)5
1k+2⋅(k+2)(k-2)5
Cancel the common factor of k+2.
Cancel the common factor.
1k+2⋅(k+2)(k-2)5
Rewrite the expression.
k-25
k-25
Simplify (1/(k+2))/(5/(k^2-4))