To solve the rational expression [tex]\(\frac{21z^2 - x - 10}{3x + 2}\)[/tex], we will follow these steps:
1. Examine the Numerator and Denominator:
Begin by looking at both the numerator [tex]\(21z^2 - x - 10\)[/tex] and the denominator [tex]\(3x + 2\)[/tex]. The goal is to simplify the expression if possible.
2. Check for Factorization:
Determine if the numerator can be factorized or simplified to make the denominator cancel out. In this case, the numerator is [tex]\(21z^2 - x - 10\)[/tex]. Given the variable terms look unrelated (where [tex]\(z\)[/tex] is different from [tex]\(x\)[/tex]), we recognize that the usual polynomial factorization techniques for quadratic equations do not directly apply here as it is not easily simplified in terms of [tex]\(x\)[/tex].
3. Simplify if Possible:
If the numerator and denominator share common factors, we could cancel them out.
In this given expression, the numerator [tex]\(21z^2 - x - 10\)[/tex] and the denominator [tex]\(3x + 2\)[/tex] have no shared factors since they contain different variables.
4. Understanding the Structure:
As it is currently given, there is no factorization or simplification directly possible due to the distinct variables in the numerator and the denominator.
Therefore, the rational expression [tex]\(\frac{21z^2 - x - 10}{3x + 2}\)[/tex] cannot be simplified further without additional context or constraints.
