To simplify the expression [tex]\( y = \frac{5}{x^3} - \frac{6}{x} \)[/tex], let's break it down into smaller steps:
1. Identify the terms: The expression is composed of two terms: [tex]\(\frac{5}{x^3}\)[/tex] and [tex]\(\frac{6}{x}\)[/tex].
2. Rewrite the terms with negative exponents:
- The first term [tex]\(\frac{5}{x^3}\)[/tex] can be rewritten as [tex]\(5x^{-3}\)[/tex].
- The second term [tex]\(\frac{6}{x}\)[/tex] can be rewritten as [tex]\(6x^{-1}\)[/tex].
3. Combine the terms using common notation:
After rewriting with negative exponents, we can write the expression as:
[tex]\[
y = 5x^{-3} - 6x^{-1}
\][/tex]
4. Summarize the simplified expression:
- The term [tex]\(\frac{5}{x^3}\)[/tex] corresponds to [tex]\(5x^{-3}\)[/tex]
- The term [tex]\(\frac{6}{x}\)[/tex] corresponds to [tex]\(6x^{-1}\)[/tex]
Putting these together, we get:
[tex]\[
y = \frac{5}{x^3} - \frac{6}{x}
\][/tex]
Therefore, the simplified form of the expression is:
[tex]\[
y = -\frac{6}{x} + \frac{5}{x^3}
\][/tex]
