Write in lowest terms (5k^2-13k-6)/(5k+2)

You've got: (5k^2-13k-6)/5k+2

then, we can break the brackets and operate the fraction
=> 5k^2-13K-6/5k+2
the K's can be cancelled out, so:
=> 5k-13-6/5+2
we operate once again:
=> 5k-19/7
and we get the result.

We want to factor the quadratic in the numerator, so we can hopefully reduce it, by canceling out the 5k + 2. You can also use polynomial division, to solve this. Anyway, by FOIL (First-Outer-Inner-Last) we gain, that the factored quadratic is (5k + 2)*(k -3). Since the 5k + 2 in the numerator cancels out with the 5k + 2 in the denominator, k - 3 is the answer.