Question

1. \\(\frac{42v^2 - 48v}{12v^2 + 6v}\\)

Explanation:

Step1: Factor numerator and denominator

Factor numerator: \(42v^2 - 48v = 6v(7v - 8)\)
Factor denominator: \(12v^2 + 6v = 6v(2v + 1)\)

Step2: Cancel common factors

Cancel \(6v\) (assuming \(v
eq0\) and \(2v + 1
eq0\)):
\(\frac{6v(7v - 8)}{6v(2v + 1)}=\frac{7v - 8}{2v + 1}\)

Answer:

\(\frac{7v - 8}{2v + 1}\) (with \(v
eq0\) and \(v
eq-\frac{1}{2}\))