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Simplifying sqrt(2x + 1) + sqrt(3x + 2) = sqrt(5x + 3) Reorder the terms: qrst(1 + 2x) + sqrt(3x + 2) = sqrt(5x + 3) (1 * qrst + 2x * qrst) + sqrt(3x + 2) = sqrt(5x + 3) (1qrst + 2qrstx) + sqrt(3x + 2) = sqrt(5x + 3) Reorder the terms: 1qrst + 2qrstx + qrst(2 + 3x) = sqrt(5x + 3) 1qrst + 2qrstx + (2 * qrst + 3x * qrst) = sqrt(5x + 3) 1qrst + 2qrstx + (2qrst + 3qrstx) = sqrt(5x + 3) Reorder the terms: 1qrst + 2qrst + 2qrstx + 3qrstx = sqrt(5x + 3) Combine like terms: 1qrst + 2qrst = 3qrst 3qrst + 2qrstx + 3qrstx = sqrt(5x + 3) Combine like terms: 2qrstx + 3qrstx = 5qrstx 3qrst + 5qrstx = sqrt(5x + 3) Reorder the terms: 3qrst + 5qrstx = qrst(3 + 5x) 3qrst + 5qrstx = (3 * qrst + 5x * qrst) 3qrst + 5qrstx = (3qrst + 5qrstx) Add '-3qrst' to each side of the equation. 3qrst + -3qrst + 5qrstx = 3qrst + -3qrst + 5qrstx Combine like terms: 3qrst + -3qrst = 0 0 + 5qrstx = 3qrst + -3qrst + 5qrstx 5qrstx = 3qrst + -3qrst + 5qrstx Combine like terms: 3qrst + -3qrst = 0 5qrstx = 0 + 5qrstx 5qrstx = 5qrstx Add '-5qrstx' to each side of the equation. 5qrstx + -5qrstx = 5qrstx + -5qrstx Combine like terms: 5qrstx + -5qrstx = 0 0 = 5qrstx + -5qrstx Combine like terms: 5qrstx + -5qrstx = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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