20244Activity 2CA"Multiplying and Dividing Rational and fI. Find the product of the following Rational Algebraic Expression 1.3x÷4•8÷9=2.2x-2÷3•2÷x²-13. x+2÷x²-14x+49​

Step-by-step explanation:To solve each part of your task, we will address the multiplication and division of the rational algebraic expressions step-by-step, simplifying as necessary.### 1. \( \frac{3x}{4} \cdot \frac{8}{9} \)To find the product, we can multiply the numerators together and the denominators together.\[\text{Product} = \frac{3x \cdot 8}{4 \cdot 9}\]Calculating the numerators and denominators:\[= \frac{24x}{36}\]Now we can simplify the fraction:\[= \frac{2x}{3}\]### 2. \( \frac{2x - 2}{3} \cdot \frac{2}{x^2 - 1} \)First, factor the numerator and denominator where possible.The numerator can be factored:\[2x - 2 = 2(x - 1)\]For the denominator:\[x^2 - 1 = (x - 1)(x + 1) \quad \text{(difference of squares)}\]Now substitute back into the multiplication:\[= \frac{2(x - 1)}{3} \cdot \frac{2}{(x - 1)(x + 1)}\]Now, cancel out the common \( (x - 1) \):\[= \frac{2 \cdot 2}{3(x + 1)} = \frac{4}{3(x + 1)}\]### 3. \( \frac{x + 2}{x^2 - 14x + 49} \)Start by factoring the denominator:The quadratic \( x^2 - 14x + 49 \) can be factored as:\[(x - 7)^2\]Thus, we rewrite the expression as:\[= \frac{x + 2}{(x - 7)^2}\]Since there are no common factors between the numerator and the denominator, that is the simplified form.### Final Answers:1. \( \frac{2x}{3} \)2. \( \frac{4}{3(x + 1)} \)3. \( \frac{x + 2}{(x - 7)^2} \)

Answered by romnickpallon | 2024-09-08