Sure, let's simplify the given expression step-by-step:
We start with the expression:
[tex]\[
\frac{4 v^2 - 6 v^3 w^6}{2 v^5 y}
\][/tex]
1. Factor the numerator:
The numerator is \(4 v^2 - 6 v^3 w^6\). We can factor out \(2 v^2\) from both terms in the numerator:
[tex]\[
2 v^2 (2 - 3 v w^6)
\][/tex]
So the expression becomes:
[tex]\[
\frac{2 v^2 \cdot (2 - 3 v w^6)}{2 v^5 y}
\][/tex]
2. Simplify the fraction:
Notice we have a common factor of \(2 v^2\) in the numerator and the denominator:
[tex]\[
\frac{2 v^2 \cdot (2 - 3 v w^6)}{2 v^5 y} = \frac{2 - 3 v w^6}{v^3 y}
\][/tex]
Here, we divide \(2 v^2\) in the numerator by \(2 v^5\) in the denominator:
[tex]\[
\frac{2 v^2}{2 v^5} = \frac{1}{v^3}
\][/tex]
3. Final simplified form:
After simplifying, the expression becomes:
[tex]\[
\frac{2 - 3 v w^6}{v^3 y}
\][/tex]
So, the simplified form of the expression is:
[tex]\[
\frac{-3 v w^6 + 2}{v^3 y}
\][/tex]
