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Sea [tex]\frac{81 x^2-36 y^2}{9 x-6 y}[/tex].

Al aplicar las reglas de cociente notable, obtenemos:

1. [tex]9 x - 6 y[/tex]
2. [tex]81 x - 6 y[/tex]
3. [tex]9 x + 6 y[/tex]
4. [tex]81 x + 6 y[/tex]

Answer :

Sure! Let's solve the given expression step-by-step.

We start with the expression:

[tex]\[
\frac{81 x^2 - 36 y^2}{9 x - 6 y}
\][/tex]

First, notice that the numerator [tex]\(81 x^2 - 36 y^2\)[/tex] is a difference of squares. The difference of squares formula is:

[tex]\[
a^2 - b^2 = (a + b)(a - b)
\][/tex]

In this case, we can identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] as follows:
[tex]\[
a = 9x \quad \text{and} \quad b = 6y
\][/tex]

Using the difference of squares formula, we rewrite the numerator:

[tex]\[
81 x^2 - 36 y^2 = (9x)^2 - (6y)^2 = (9x + 6y)(9x - 6y)
\][/tex]

So, the given expression becomes:

[tex]\[
\frac{(9x + 6y)(9x - 6y)}{9x - 6y}
\][/tex]

Now, we can see that the term [tex]\(9x - 6y\)[/tex] appears in both the numerator and the denominator. We can cancel these terms out:

[tex]\[
\frac{(9x + 6y)(9x - 6y)}{9x - 6y} = 9x + 6y
\][/tex]

Therefore, the simplified form of the expression is:

[tex]\[
9x + 6y
\][/tex]

So, the correct choice is:

3) [tex]\(9 x + 6 y\)[/tex]

I hope this helps! If you have any more questions, feel free to ask.

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Rewritten by : Barada

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