please show step by step and explain i wouls like to see how

please show step by step and explain i wouls like to see how you got the answer

Q1. SOLVE

radical (2x+3)-radical (x+5)=1

Solution

(2x +3) - (x+5) = 1 so that [(2x +3) - (x+5) ]² = (1)² or, (2x +3) - 2(2x +3)(x+5) + (x +5) = 1 or, 3x + 8 - 2(2x +3)(x+5) = 1 or, 3x + 7 - 2(2x +3)(x+5) = 0 so that 2(2x +3)(x+5) = 3x +7. Therefore, [2(2x +3)(x+5)]² = (3x +7)² or, 4(2x +3)(x + 5) = 9x² + 42x + 49 or, 4( 2x²+ 13x +15) =   9x² + 42x + 49 or, 8x² +52x +60 = 9x² + 42x + 49 or, 9x² -8x² +42x -52x + 49 – 60 = 0 or, x² -10x -11 = 0 or, x² -11x+x -11 = 0 or, x(x – 11) +1 (x -11) = 0 or, (x -11)(x +1) = 0 so that either x = 11 or x = -1. On verifying the answers, we have, when x = 11, (2x +3) - (x+5) = 25 - 16 = 5 -4 = 1, so that x = 11 is a correct answer. Also, if x = -1, then (2x +3) - (x+5) = 1 - 4 = 1 -2 = -1 which is incorrect. Therefore, the answer is x = 11.