Sure! Let's go through each expression step by step.
### Expression 1: [tex]\(\frac{r s}{3}+\frac{x y}{7}\)[/tex]
1. Identify the terms:
- The first term is [tex]\(\frac{r s}{3}\)[/tex].
- The second term is [tex]\(\frac{x y}{7}\)[/tex].
2. Combine the terms:
- Since these terms do not have a common denominator, we simply write them as they are.
- The overall expression remains [tex]\(\frac{r s}{3} + \frac{x y}{7}\)[/tex].
So, the first expression in its simplified form is:
[tex]\[ \frac{r s}{3} + \frac{x y}{7} \][/tex]
### Expression 2: [tex]\(3 x^4 + 9 x^3 - 4 x^5 + 1\)[/tex]
1. Identify the terms:
- The polynomial given is [tex]\(3 x^4 + 9 x^3 - 4 x^5 + 1\)[/tex].
2. Arrange the terms:
- We usually write polynomials in descending order of the powers of [tex]\(x\)[/tex].
- So, we rearrange the terms as [tex]\( -4 x^5 + 3 x^4 + 9 x^3 + 1 \)[/tex].
This polynomial is already simplified and arranged in standard form. Thus, the second expression is:
[tex]\[ -4 x^5 + 3 x^4 + 9 x^3 + 1 \][/tex]
### Summary
The final forms of the given mathematical expressions are:
1. [tex]\(\frac{r s}{3} + \frac{x y}{7}\)[/tex]
2. [tex]\(-4 x^5 + 3 x^4 + 9 x^3 + 1\)[/tex]
These expressions are fully simplified and properly organized.
