Answer :

Sure, let's simplify the expression [tex]\(y = \left(\frac{21}{x^6} - 3 x^{11}\right)\)[/tex] step-by-step:

1. Start with the given expression:

[tex]\[ y = \frac{21}{x^6} - 3 x^{11} \][/tex]

2. Combine the terms using a common denominator:

We notice that both terms can be written with a common denominator of [tex]\(x^6\)[/tex]. This means we can rewrite the expression as a single fraction.

[tex]\[ y = \frac{21}{x^6} - \frac{3 x^{11} \cdot x^6}{x^6} \][/tex]

3. Simplify the second term in the numerator:

We multiply [tex]\(3 x^{11}\)[/tex] by [tex]\(x^6\)[/tex] in the numerator:

[tex]\[ 3 x^{11} \cdot x^6 = 3 x^{17} \][/tex]

So the expression becomes:

[tex]\[ y = \frac{21}{x^6} - \frac{3 x^{17}}{x^6} \][/tex]

4. Combine under a single denominator:

[tex]\[ y = \frac{21 - 3 x^{17}}{x^6} \][/tex]

5. Factor out any common terms in the numerator:

The numerator [tex]\(21 - 3 x^{17}\)[/tex] can be factored:

[tex]\[ 21 - 3 x^{17} = 3(7 - x^{17}) \][/tex]

Now the expression is:

[tex]\[ y = \frac{3 (7 - x^{17})}{x^6} \][/tex]

6. Write the final simplified expression:

[tex]\[ y = \frac{3 (7 - x^{17})}{x^6} \][/tex]

So, the simplified form of [tex]\( \left(\frac{21}{x^6} - 3 x^{11}\right) \)[/tex] is:

[tex]\[ y = \frac{3 (7 - x^{17})}{x^6} \][/tex]