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
Let's knock this out. To simplify the expression, we will find a common denominator and combine the fractions. Step 1: Combine the fractions using a common denominator. The common denominator is the product of the two denominators, (sqrt(17) - 2sqrt(5))(sqrt(17) + 2sqrt(5)). (1)/(sqrt(17) - 25) - (1)/(sqrt(17) + 25) = (sqrt(17) + 2sqrt(5)) - (sqrt(17) - 2sqrt(5))(sqrt(17) - 2sqrt(5))(sqrt(17) + 2sqrt(5)) Step 2: Simplify the numerator. (sqrt(17) + 2sqrt(5)) - (sqrt(17) - 2sqrt(5)) = sqrt(17) + 2sqrt(5) - sqrt(17) + 2sqrt(5) = ( sqrt(17) - sqrt(17) ) + ( 2sqrt(5) + 2sqrt(5) ) = 0 + 4sqrt(5) = 4sqrt(5) Step 3: Simplify the denominator using the difference of squares formula, (a-b)(a+b) = a^2 - b^2. Here, a = sqrt(17) and b = 2sqrt(5). (sqrt(17) - 2sqrt(5))(sqrt(17) + 2sqrt(5)) = (sqrt(17))^2 - (2sqrt(5))^2 = 17 - (2^2 · (sqrt(5))^2) = 17 - (4 · 5) = 17 - 20 = -3 Step 4: Substitute the simplified numerator and denominator back into the expression. 4sqrt(5)-3 Step 5: Write the final simplified expression. -4sqrt(5)3 Send me the next one 📸