Answer :

GinnyAnswer
Certainly! Let's simplify the given expression step by step:

[tex]\[ \frac{x^4 - 6x^2 - 1}{x^2} \][/tex]

1. Breakup the expression: We can break up the numerator into individual terms divided by the denominator.

[tex]\[ \frac{x^4 - 6x^2 - 1}{x^2} = \frac{x^4}{x^2} - \frac{6x^2}{x^2} - \frac{1}{x^2} \][/tex]

2. Simplify each term individually:
- Simplify [tex]\(\frac{x^4}{x^2}\)[/tex]:
[tex]\[ \frac{x^4}{x^2} = x^{4 - 2} = x^2 \][/tex]

- Simplify [tex]\(\frac{6x^2}{x^2}\)[/tex]:
[tex]\[ \frac{6x^2}{x^2} = 6 \quad (\text{since } x^2/x^2 \text{ cancels out}) \][/tex]

- Simplify [tex]\(\frac{1}{x^2}\)[/tex]:
[tex]\[ \frac{1}{x^2} \quad (\text{this term remains as it is}) \][/tex]

3. Combine the simplified terms:
Now we can combine the simplified parts back together:

[tex]\[ x^2 - 6 - \frac{1}{x^2} \][/tex]

Therefore, the simplified form of the expression

[tex]\[ \frac{x^4 - 6x^2 - 1}{x^2} \][/tex]

is

[tex]\[ x^2 - 6 - \frac{1}{x^2} \][/tex]
Hi1315

Answer:

[tex]x^2 - 6 - \frac{1}{x^2}[/tex]

Step-by-step explanation:

To simplify the expression[tex]\frac{x^4 - 6x^2 - 1}{x^2}[/tex], we can divide each term in the numerator by x²:

[tex]\dfrac{x^4 - 6x^2 - 1}{x^2} \\\\ \dfrac{x^4}{x^2} - \dfrac{6x^2}{x^2} - \dfrac{1}{x^2}[/tex]

Now, simplify each term:

[tex]\frac{x^4}{x^2} = x^{4-2} = x^2\\\\\frac{6x^2}{x^2} = 6\\\\\frac{1}{x^2} = x^{-2}[/tex]

Putting it all together:

[tex]\frac{x^4 - 6x^2 - 1}{x^2} \\\\x^2 - 6 - \frac{1}{x^2}[/tex]

So, the simplified form of the expression is:

[tex]x^2 - 6 - \frac{1}{x^2}[/tex]

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