Final answer:
To factor the given trinomial x²/4y² - 2/3 + 4y²/9x², first find a common denominator for the terms. Rearrange the terms and combine them, then simplify and factor out the common factor to get the final expression.
Step-by-step explanation:
To factor the given trinomial, x²/4y² - 2/3 + 4y²/9x², we can first find a common denominator for the terms.
The common denominator is 36x²y². Rearranging the terms, we get (9x^2 - 4y^2)/(36x^2y^2) - 24/(36x^2y^2) + (16y^2)/(36x^2y^2).
Now, we can combine the terms by adding or subtracting the numerators and keeping the common denominator, giving us (9x^2 - 4y^2 - 24 + 16y^2)/(36x^2y^2).
Simplifying further, we have (9x^2 + 12y^2 - 24)/(36x^2y^2).
Finally, factoring out the common factor of 3 from the numerator, we get 3(3x^2 + 4y^2 - 8)/(36x^2y^2), which can be written as 3(3x^2 + 4y^2 - 8)/(4xy)^2.
Learn more about Factoring trinomials