Questions: Worksheets are graded on completion. Please check the solutions to make sure you understand the problems. 1. (5 * 4 * 11) / (15 * 2 * 9) 2. (x^2 - 4x + 4) / (x^2 + 6x - 16)

Solution Steps

Simplify the fraction \(\frac{5 \cdot 4 \cdot 11}{15 \cdot 2 \cdot 9}\) by canceling common factors in the numerator and denominator.

\[ \frac{5 \cdot 4 \cdot 11}{15 \cdot 2 \cdot 9} = \frac{5 \cdot 4 \cdot 11}{15 \cdot 2 \cdot 9} = \frac{220}{270} \]

Divide the numerator and denominator by their greatest common divisor (GCD), which is 10.

\[ \frac{220}{270} = \frac{220 \div 10}{270 \div 10} = \frac{22}{27} \]

Factor the numerator and denominator of the rational expression \(\frac{x^{2}-4x+4}{x^{2}+6x-16}\).

• Numerator: \(x^{2}-4x+4 = (x-2)^2\)
• Denominator: \(x^{2}+6x-16 = (x+8)(x-2)\)

\[ \frac{x^{2}-4x+4}{x^{2}+6x-16} = \frac{(x-2)^2}{(x+8)(x-2)} \]

Cancel the common factor \((x-2)\) in the numerator and denominator.

\[ \frac{(x-2)^2}{(x+8)(x-2)} = \frac{x-2}{x+8} \]

Final Answer