Answer:

To simplify the expression [tex](8x^2 - 18y^2) / (2x - 3y)[/tex], we can factor out common terms from the numerator and denominator.

First, let's factor out 2 from the numerator and 3 from the denominator:

[tex](8x^2 - 18y^2) / (2x - 3y) = 2(4x^2 - 9y^2) / 3(2x - 3y)[/tex]

Next, we can factor the numerator further using the difference of squares formula:

[tex](8x^2 - 18y^2) = 2(2x)^2 - 2(3y)^2 = 2(2x + 3y)(2x - 3y)[/tex]

Now, we can substitute this back into the expression:

[tex]2(4x^2 - 9y^2) / 3(2x - 3y) = 2(2x + 3y)(2x - 3y) / 3(2x - 3y)[/tex]

Notice that the (2x - 3y) terms in the numerator and denominator cancel out:

[tex]2(2x + 3y)(2x - 3y) / 3(2x - 3y) = 2(2x + 3y) / 3[/tex]

Therefore, the simplified expression is [tex]2(2x + 3y) / 3.[/tex]

Answer:

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