Math  /  Algebra

Question Simplify the expression x2+5x36x28x+16\frac{x^{2}+5 x-36}{x^{2}-8 x+16} and determine which of the following statements are true: 1) It could represent the difference of xx4\frac{x}{x-4} and 9x4\frac{-9}{x-4}. 2) It could represent the product of x+9(x4)2\frac{x+9}{(x-4)^{2}} and (x4)(x-4). 3) It could represent the sum of a2+5ax28x\frac{a^{2}+5 a}{x^{2}-8 x} and 3616\frac{-36}{16}. 4) It could represent the quotient of (x9)(x-9) and (x4)(x-4). 5) It is equivalent to the rational expression x+9x4\frac{x+9}{x-4}.

Studdy Solution
To summarize, the true statements are:
1. The expression could represent the difference of xx4\frac{x}{x-4} and 9x4\frac{-9}{x-4}.
2. The expression could represent the product of x+9(x4)2\frac{x+9}{(x-4)^{2}} and (x4)(x-4).
5. The expression is equivalent to the rational expression x+9x4\frac{x+9}{x-4}.

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