Example 3 How to Simplify a Complex Rational Expression Using Method Il Simplify: 2+ 3 Step-by-Step Solution Step 1Find the least common denominator of all the denominators in the complex rational expression. The denominators of the complex rational expression are 3, x, and 2. The least common denominator is 2 . 3 . x = 6x. Step 2Multiply both the numerator and the denominator of the complex rational expression by the LCD found in Step 1. 1 1 6x = (3+2).6x 6x 2 (243 ) .6x Distribute 6x to each term: = 1 Step 3:Simplify the rational expression. Simplify: = 2x +6 3ac (2 + 3) 2 ( 2 43) Factor and divide out common factors: = 2Example 1 How to Simplify a Complex Rational Expression Using Method! (18 i Simplify: If; 2 mil Step-by-Step Solution Notice that X cannot equal 3 because that would make the denominator, \"3 , equal zero; x cannot equal 0 because it would make the expression 1 l in the numerator undefined. Step 1Write the numerator of the complex rational expression as a single rational expression. The least common denominator of % and i is 3x. 1 1 _;. l. 5+; 3 J:+a: 3 i i 3x+3$ g _a+b._ :B+3 c+cc' 3w Step 2Write the denominator of the complex This is already done. rational expression as a single rational expression. Step 3Rewrite the complex rational expression using the rational expressions found in Steps 1 and 2. 23773 l__i 3 .1: (c773 2:773 2 2 Step 4Simp|ify the rational expression using the techniques for dividing rational expressions from Section 5.1 El. Lesson 6 Critical Thinking Questions \"4 WRITE OUT DETAILED RESPONSES TO EACH OF THESE CRITICAL THINKING QUESTIONS. 10 Points Total 1. Using the language of the \"Work Smart" tip on page 402 of your textbook, explain to a mistaken novice Intermediate Algebra student you are tutoring why 2 z +3$+5 : (1)2 + 1 \"+5 Is false. 2. Section 5-3 in your textbook talks about two ways for solving Complex Rational Expressions, Method | on page 420 and Method II on page 422. Solve the following using BOTH METHODS, which you SHOW CLEARLY HERE, and then discuss which method you prefer using going forward (and why): Sac1+ 31'1 9:5'2 731': 3. If x and y represent two quantities and k is a non-zero number, explain the difference between being told that y varies directly with x and y varies inversely with x