Question

simplify.
\frac{30k^2 + 6k}{5k + k}
a k + 1
b 5k + 1
c 6k + 1
d 6k + 6

Explanation:

Step1: Simplify numerator and denominator

First, factor the numerator \(30k^2 + 6k\). We can factor out a common factor of \(6k\) from both terms:
\(30k^2 + 6k = 6k(5k + 1)\)
Next, simplify the denominator \(5k + k\). Combine like terms:
\(5k + k = 6k\)

Step2: Divide the simplified numerator by the simplified denominator

Now we have the fraction \(\frac{6k(5k + 1)}{6k}\). Assuming \(k
eq0\) (since if \(k = 0\), the original denominator would be \(0\) which is undefined), we can cancel out the common factor of \(6k\) from the numerator and the denominator:
\(\frac{6k(5k + 1)}{6k}=5k + 1\)

Answer:

B. \(5k + 1\)