Written in simplest form, the expression [tex]\frac{x^2 y^2 - 9}{3 - xy}[/tex] is equivalent to:

1. -1
2. [tex]\frac{1}{3 + xy}[/tex]
3. -(3 + xy)
4. 3 + xy

Please show work.

((x^2)(y^2) - 9) *(3 - xy).
Note difference of two squares: (a^2 - b^2) = (a-b)(a+b) (x^2)(y^2) - 9 = (xy)^2 - 3 ^2 = (xy - 3)(xy + 3). (Take note)
(3- xy) = -(xy - 3). (Take note of this also)
Your question said: ((x^2)(y^2) - 9) times (3 - xy), Don't you think it should be divide ? Would solve it as divide.
((x^2)(y^2) - 9) /(3 - xy) = (xy - 3)(xy + 3) / -(xy - 3)
= -(xy + 3).
Answer is (3). Solved it as divide. Using times gives none of the solution among the options. Cheers.

Answered by olemakpadu | 2024-06-10

The expression 3 − x y x 2 y 2 − 9 ​ simplifies to - (3 + xy) after factoring and using properties of negative signs. Therefore, the correct answer is option 3. This is achieved by recognizing the numerator as a difference of squares and rewriting the denominator appropriately.
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Answered by olemakpadu | 2024-12-26