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
Step 1: Use the given x to find x and x. Given x = (12)/(5). In a right-angled triangle, x = OppositeAdjacent. Let the opposite side be 12k and the adjacent side be 5k for some constant k. Using the Pythagorean theorem, the hypotenuse H is: H = sqrt((12k)^2 + (5k)^2) = sqrt(144k^2 + 25k^2) = sqrt(169k^2) = 13k Now, we can find x and x: x = OppositeHypotenuse = (12k)/(13k) = (12)/(13) x = AdjacentHypotenuse = (5k)/(13k) = (5)/(13) Step 2: Substitute the values of x and x into the expression. The expression is ( x + 2 x)/(1 - x). Substitute x = (12)/(13) and x = (5)/(13): (12)/(13) + 2 ((5)/(13))1 - (12)/(13) Step 3: Simplify the numerator. (12)/(13) + 2 ((5)/(13)) = (12)/(13) + (10)/(13) = (12+10)/(13) = (22)/(13) Step 4: Simplify the denominator. 1 - (12)/(13) = (13)/(13) - (12)/(13) = (13-12)/(13) = (1)/(13) Step 5: Divide the simplified numerator by the simplified denominator. (22)/(13)(1)/(13) = (22)/(13) × (13)/(1) = 22 The value of the expression is 22. Send me the next one 📸