This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To simplify the given continued fraction, we will work from the innermost expression outwards. The expression is: (1)/(2 - 1)2 - (1)/(2 - x) Step 1: Simplify the innermost denominator. The innermost denominator is 2 - x. This cannot be simplified further. Step 2: Simplify the expression 2 - (1)/(2 - x). To combine these terms, we find a common denominator. 2 - (1)/(2 - x) = (2(2 - x))/(2 - x) - (1)/(2 - x) = (4 - 2x - 1)/(2 - x) = (3 - 2x)/(2 - x) Step 3: Simplify the fraction (1)/(2 - 1)2 - x. We use the result from Step 2. (1)/(2 - 1)2 - x = (1)/(3 - 2x)2 - x To divide by a fraction, we multiply by its reciprocal. (1)/(3 - 2x)2 - x = (2 - x)/(3 - 2x) Step 4: Simplify the expression 2 - (1)/(2 - 1)2 - x. We use the result from Step 3. 2 - (2 - x)/(3 - 2x) Again, find a common denominator. (2(3 - 2x))/(3 - 2x) - (2 - x)/(3 - 2x) = (6 - 4x - (2 - x))/(3 - 2x) = (6 - 4x - 2 + x)/(3 - 2x) = (4 - 3x)/(3 - 2x) Step 5: Simplify the entire expression (1)/(2 - 1)2 - (1)/(2 - x). We use the result from Step 4. (1)/(4 - 3x)3 - 2x Multiply by the reciprocal. (1)/(4 - 3x)3 - 2x = (3 - 2x)/(4 - 3x) The simplified expression is: (3 - 2x)/(4 - 3x) Send me the next one 📸