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
You're on a roll — To find the value of (x+y), we first need to simplify the given expression and then compare it to x + ysqrt(15) to find x and y. Step 1: Simplify the left-hand side of the equation sqrt(3)+sqrt(5)sqrt(5). We can split the fraction into two terms: sqrt(3)+sqrt(5)sqrt(5) = sqrt(3)sqrt(5) + sqrt(5)sqrt(5) = sqrt(3)sqrt(5) + 1 Step 2: Rationalize the denominator of the term sqrt(3)sqrt(5). Multiply the numerator and the denominator by sqrt(5): sqrt(3)sqrt(5) × sqrt(5)sqrt(5) = sqrt(3 × 5)5 = sqrt(15)5 Step 3: Substitute the rationalized term back into the expression. sqrt(15)5 + 1 Rearrange the terms to match the form x + ysqrt(15): 1 + (1)/(5)sqrt(15) Step 4: Compare this simplified expression with x + ysqrt(15). 1 + (1)/(5)sqrt(15) = x + ysqrt(15) By comparing the constant terms and the coefficients of sqrt(15), we can identify x and y: x = 1 y = (1)/(5) Step 5: Calculate the value of (x+y). x+y = 1 + (1)/(5) To add these, find a common denominator: x+y = (5)/(5) + (1)/(5) = (5+1)/(5) = (6)/(5) Convert the improper fraction to a mixed number: (6)/(5) = 1(1)/(5) Comparing this result with the given options: A. 1(3)/(5) B. 1(2)/(5) C. 1(1)/(5) D. (1)/(5) The correct option is C. The final answer is C. 1(1)/(5). Drop the next question!