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(12 x-x^(2))/(x^(2)-10 x-24) Which expression is equivalent to the given expression for all x < 10 ? Choose 1 answer: (A) -(x)/(x-2) (B) (x)/(x-2) (C) (x)/(x+2) (D) -(x)/(x+2)

12x−x2x2−10x−24 \frac{12 x-x^{2}}{x^{2}-10 x-24} \newlineWhich expression is equivalent to the given expression for all x<10 ?\newlineChoose 11 answer:\newline(A) −xx−2 -\frac{x}{x-2} \newline(B) xx−2 \frac{x}{x-2} \newline(C) xx+2 \frac{x}{x+2} \newline(D) −xx+2 -\frac{x}{x+2}

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Q. 12x−x2x2−10x−24 \frac{12 x-x^{2}}{x^{2}-10 x-24} \newlineWhich expression is equivalent to the given expression for all x<10 x<10 ?\newlineChoose 11 answer:\newline(A) −xx−2 -\frac{x}{x-2} \newline(B) xx−2 \frac{x}{x-2} \newline(C) xx+2 \frac{x}{x+2} \newline(D) −xx+2 -\frac{x}{x+2}
  1. Factorize Numerator and Denominator: First, factorize the numerator and denominator.\newlineNumerator: 12x−x2=x(12−x)12x - x^2 = x(12 - x)\newlineDenominator: x2−10x−24=(x−12)(x+2)x^2 - 10x - 24 = (x - 12)(x + 2)
  2. Rewrite with Factored Forms: Rewrite the expression with the factored forms. 12x−x2x2−10x−24=x(12−x)(x−12)(x+2) \frac{12x - x^2}{x^2 - 10x - 24} = \frac{x(12 - x)}{(x - 12)(x + 2)}
  3. Simplify by Canceling Factors: Simplify the expression by canceling common factors. x(12−x)/((x−12)(x+2))=−x(x−12)/((x−12)(x+2))x(12 - x) / ((x - 12)(x + 2)) = -x(x - 12) / ((x - 12)(x + 2))
  4. Cancel Common Terms: Cancel the (x−12)(x - 12) terms. −xx+2-\frac{x}{x + 2}
  5. Check Simplified Expression: Check the simplified expression. The simplified expression is −xx+2-\frac{x}{x + 2}

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