Certainly! Let's solve the given mathematical expression step-by-step.
Given the expression for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{2}{(3 - 2x)^2} \][/tex]
1. Expression Overview:
- We have [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
- The denominator is [tex]\((3 - 2x)^2\)[/tex], a squared term.
2. Analyzing the Function:
- The expression is a rational function where the numerator is [tex]\( 2 \)[/tex] and the denominator is [tex]\( (3 - 2x)^2 \)[/tex].
3. Simplifying the Denominator:
- The denominator [tex]\( (3 - 2x)^2 \)[/tex] expands to [tex]\( (3 - 2x)(3 - 2x) \)[/tex], but we keep it in the squared form for simplicity in this context.
4. Final Expression:
- The numerator remains as [tex]\( 2 \)[/tex].
- The denominator remains as [tex]\( (3 - 2x)^2 \)[/tex].
So, consolidating everything, the expression for [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{2}{(3 - 2x)^2} \][/tex]
This is the detailed breakdown of the given expression.
