-5k + 15
_________
k2 - 9
Does this facot to -5(K+3)
_______
k^2 -9 Is this right?
Nope. You have to factor the denominator to (k+3)(k-3)
The numerator you factored should have been -5(k-3), you missed a sign.
To factor the denominator, we can use the difference of squares formula:
k^2 - 9 = (k + 3)(k - 3)
Now let's rewrite the fraction with the factored denominator:
(-5k + 15) / (k^2 - 9) = (-5(k - 3)) / ((k + 3)(k - 3))
Notice that the (k - 3) terms in the numerator and denominator cancel out:
= -5 / (k + 3)
So the correct factored form of the expression is:
-5 / (k + 3)