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
To leave the answer in surd form, we need to rationalize the denominator. Step 1: Write the given expression. (2)/(sqrt(5)-7) Step 2: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of sqrt(5)-sqrt(7) is sqrt(5)+sqrt(7). (2)/(sqrt(5)-7) × sqrt(5)+sqrt(7)sqrt(5)+sqrt(7) Step 3: Perform the multiplication. Use the difference of squares formula (a-b)(a+b) = a^2 - b^2 for the denominator. 2(sqrt(5)+sqrt(7))(sqrt(5)-sqrt(7))(sqrt(5)+sqrt(7)) = 2(sqrt(5)+sqrt(7))(sqrt(5))^2 - (sqrt(7))^2 Step 4: Simplify the denominator. 2(sqrt(5)+sqrt(7))5 - 7 = 2(sqrt(5)+sqrt(7))-2 Step 5: Simplify the fraction by dividing the numerator by the denominator. 2(sqrt(5)+sqrt(7))-2 = -(sqrt(5)+sqrt(7)) Step 6: Distribute the negative sign. -(sqrt(5)+sqrt(7)) = -sqrt(5)-sqrt(7) The simplified expression in surd form is -sqrt(5)-sqrt(7). -sqrt(5)-sqrt(7) Last free one today — make it count tomorrow, or type /upgrade for unlimited.