To solve and simplify the given mathematical expression [tex]\(\frac{7x - 3}{x + 2}\)[/tex], we will go through the following steps:
1. Understanding the Expression:
- The numerator of the fraction is [tex]\(7x - 3\)[/tex].
- The denominator of the fraction is [tex]\(x + 2\)[/tex].
2. Simplifying:
- In this case, the expression [tex]\(\frac{7x - 3}{x + 2}\)[/tex] is already in its simplest form because there are no common factors between the numerator and the denominator that can be canceled out.
3. Domain Considerations:
- It's important to note the domain of the expression. The denominator [tex]\(x + 2\)[/tex] cannot be zero because division by zero is undefined.
- Therefore, [tex]\(x + 2 \neq 0\)[/tex], which implies [tex]\(x \neq -2\)[/tex].
4. Final Expression:
- After confirming that it is in its simplest form and considering the domain, the simplified expression remains [tex]\(\frac{7x - 3}{x + 2}\)[/tex].
In conclusion, the expression [tex]\(\frac{7x - 3}{x + 2}\)[/tex] is already simplified and valid for all [tex]\(x\)[/tex] except [tex]\(x = -2\)[/tex]. This is the final result.
