Question

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

Explanation:

Step1: Factor numerator and denominator

Numerator: \(30k^2 + 6k = 6k(5k + 1)\)
Denominator: \(5k + k = 6k\) (Wait, no, \(5k + k = 6k\)? Wait, original denominator is \(5k + k\)? Wait, maybe a typo? Wait, looking at the problem, maybe denominator is \(5k + 1\)? Wait, no, the user's image shows \(\frac{30k^2 + 6k}{5k + k}\)? Wait, no, maybe it's \(\frac{30k^2 + 6k}{5k + 1}\)? Wait, no, let's check again. Wait, the numerator is \(30k^2 + 6k\), denominator is \(5k + k\)? Wait, \(5k + k = 6k\), so then:

Wait, if denominator is \(5k + k = 6k\), then:

Step2: Simplify the fraction

\(\frac{6k(5k + 1)}{6k}\) (assuming numerator factors to \(6k(5k + 1)\) and denominator is \(6k\))
Cancel out \(6k\) (assuming \(k
eq 0\)): \(5k + 1\)

Wait, but maybe the denominator is \(5k + 1\)? Wait, the original problem's denominator: maybe a typo, but based on the options, let's re - check. Wait, the numerator: \(30k^2+6k = 6k(5k + 1)\). If the denominator is \(5k + 1\), then:

Step1 (corrected): Factor numerator and denominator

Numerator: \(30k^2 + 6k=6k(5k + 1)\)
Denominator: \(5k + 1\)

Step2 (corrected): Simplify

\(\frac{6k(5k + 1)}{5k + 1}=6k\)? No, that's not matching options. Wait, maybe the original problem's denominator is \(5k + k\) (which is \(6k\)) and numerator is \(30k^2+6k = 6k(5k + 1)\). Then:

\(\frac{6k(5k + 1)}{6k}=5k + 1\), which is option B.

Answer:

B. \(5k + 1\)