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Which of the following is equal to the rational expression when x*-2 or 3?

x²+5x+6
x²-x-6
A. X+2/X-3
B. X+3/X-3
C. x+2/x-2
D. X+3/X-2

User BPizzi
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1 Answer

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Final answer:

The rational expression (x² + 5x + 6) / (x² - x - 6) simplifies to B. x + 3 / x - 3 after factoring and canceling out common factors.

Step-by-step explanation:

The given problem requires simplifying a rational expression, which is a part of algebra in mathematics. To find which of the given options is equal to the expression (x² + 5x + 6) / (x² - x - 6), we need to factor both the numerator and denominator. Factorization of a quadratic expression is done by finding two numbers that multiply to give the product of the coefficient of and the constant term, and add to give the coefficient of x.

Let's factor both numerator and denominator:

  • Numerator: x² + 5x + 6 = (x + 2)(x + 3)
  • Denominator: x² - x - 6 = (x - 3)(x + 2)

After factoring, the expression simplifies to:

(x + 2)(x + 3) / (x - 3)(x + 2)

We observe that (x + 2) is in both the numerator and denominator, so they cancel each other out. The simplified form of the expression will be:

(x + 3) / (x - 3)

Therefore, the correct answer is B. x + 3 / x - 3.

User Rzwnahmd
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