https://file.aiquickdraw.com/mathbot/file/1725534468712z8on0umv.jpg

The given equation from the image is:

\[
y = \frac{5}{(3x + 1)(7x - 2)}
\]

This is a rational function where \( y \) is expressed as the quotient of a constant 5 and the product of two linear expressions, \( (3x + 1) \) and \( (7x - 2) \).

### Key Aspects:
- **Numerator**: \( 5 \) is a constant.
- **Denominator**: The denominator is the product of two factors, \( (3x + 1) \) and \( (7x - 2) \), both of which are linear terms in \( x \).

To explore the properties of this function further:
1. **Domain**: The domain excludes values of \( x \) where the denominator equals zero. We solve:
   \[
   (3x + 1)(7x - 2) = 0
   \]
   This gives:
   \[
   3x + 1 = 0 \quad \text{or} \quad 7x - 2 = 0
   \]
   Solving for \( x \):
   \[
   x = -\frac{1}{3} \quad \text{or} \quad x = \frac{2}{7}
   \]
   So, the domain of \( y \) is all real numbers except \( x = -\frac{1}{3} \) and \( x = \frac{2}{7} \).

2. **Vertical Asymptotes**:

Explore the properties of the rational function y = 5 / [(3x + 1)(7x - 2)], including how to find the domain and determine the vertical asymptotes. This example covers key algebraic concepts for students in Grades 9-12.

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