Question

Сократите дробь: x^2−24x−81 /x−27

Answer 1

Ответ:

$x + 3$

Объяснение:

$\frac{ {x}^{2} - 24x - 81}{x - 27} = \frac{ {x}^{2} + 3x - 27x - 81}{x - 27} = \frac{x(x + 3) - 27(x + 3)}{x - 27} = \frac{(x + 3)(x - 27)}{x - 27} = x + 3$

Answer 2

To simplify the given expression, we can use long division or synthetic division. Let's use long division:

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       x + 3
   ____________________

x - 27 | x^2 - 24x - 81 -(x^2 - 27x) ____________ 3x - 81 -(3x - 81) __________ 0

The result of the long division is (x + 3), and the remainder is 0, indicating that the expression (x^2 - 24x - 81)/(x - 27) is fully divisible. So, the simplified form of the expression is:

(x^2 - 24x - 81)/(x - 27) = x + 3