Rút gọn \[ \sqrt{\frac{1-3x}{2x} + \frac{3x-2}{2x-1} + \frac{3x-2}{2x-4x^2}} \] \[ y) \frac{x^2}{x+y} + \frac{y^2}{y+z} - \frac{z^2}{x+y} + \frac{-z^2}{y+z} ; \] Tham khảo câu trả lời từ Trợ lý ảo Lazi To simplify the given expression, we can break it down into parts. ### Step 1: Simplifying 1. **Expression**: \[ \sqrt{\frac{1 - 3x}{2x} + \frac{3x - 2}{2x - 1} + \frac{3x - 2}{2x - 4x^2}} \] 2. **Combine the fractions**: - Find a common denominator for the fractions inside the square root. ### Step 2: Simplifying each term - **First term**: \[ \frac{1 - 3x}{2x} \] - **Second term**: \[ \frac{3x - 2}{2x - 1} \] - **Third term**: \[ \frac{3x - 2}{2x - 4x^2} = \frac{3x - 2}{2x(1 - 2x)} \] ### Step 3: Finding a common denominator The common denominator would be \(2x(2x - 1)(1 - 2x)\). ### Step 4: Combine everything under the square root 1. Multiply each term by the appropriate factor: - Adjust fractions to have the common denominator. 2. Combine and then simplify the resulting single fraction. ### Step 5: Factor and simplify under the square root 3. Look for possible simplifications or factorization inside the square root, then compute the square root if possible. Following these steps should yield a simplified expression. For parts y), z), and J): - You will apply similar methods of combining fractions and simplifying the whole expressions. If you need detailed steps for y), z), or J), please let me know!