1k+25k2-4

Multiply the numerator by the reciprocal of the denominator.

1k+2⋅k2-45

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.

1k+2⋅(k+2)(k-2)5

Rewrite the expression.

k-25

k-25

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