simplify k squared plus 6k-1 all divided by k+5
To simplify the expression (k^2 + 6k - 1)/(k + 5), we can use polynomial long division or factoring.
Let's start with polynomial long division:
1. Divide k^2 by k: (k^2 + 6k - 1)/(k + 5) = k.
2. Multiply k by (k + 5): k * (k + 5) = k^2 + 5k.
3. Subtract the above result from the numerator (k^2 + 6k - 1): (k^2 + 6k - 1) - (k^2 + 5k) = k - 1k - 1.
Simplified, the numerator becomes: -k - 1.
4. Bring down the -1 from the numerator: -1.
5. Continue the division process with the new numerator (-k - 1).
Now we have (-k - 1)/(k + 5). To further simplify the expression, we can use factoring:
1. Factor out -1 from the numerator: -1(k + 1).
2. The simplified expression becomes: -(k + 1)/(k + 5).
Therefore, the simplified form of (k^2 + 6k - 1)/(k + 5) is -(k + 1)/(k + 5).