Question

simplify.
\\(\frac{12w^2 - 28w}{4w^2 - 8w}\\)

Explanation:

Step1: Factor numerator and denominator

Factor out the greatest common factor (GCF) from the numerator \(12w^2 - 28w\) and the denominator \(4w^2 - 8w\).
For the numerator: The GCF of \(12w^2\) and \(-28w\) is \(4w\). So, \(12w^2 - 28w = 4w(3w - 7)\).
For the denominator: The GCF of \(4w^2\) and \(-8w\) is \(4w\). So, \(4w^2 - 8w = 4w(w - 2)\).
Now the expression becomes \(\frac{4w(3w - 7)}{4w(w - 2)}\).

Step2: Cancel common factors

We can cancel out the common factor \(4w\) from the numerator and the denominator (assuming \(w
eq0\) and \(w
eq2\) to avoid division by zero).
After canceling \(4w\), we get \(\frac{3w - 7}{w - 2}\).

Answer:

\(\frac{3w - 7}{w - 2}\) (for \(w
eq0\) and \(w
eq2\))