To simplify the expression, rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of sqrt(7) + sqrt(2) is $sqrt(7) - sqrt(2)

Step 1: To simplify the expression, rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of sqrt(7) + sqrt(2) is sqrt(7) - sqrt(2). (1)/(sqrt(7) + 2) × sqrt(7) - sqrt(2)sqrt(7) - sqrt(2) Step 2: Multiply the numerators. 1 × (sqrt(7) - sqrt(2)) = sqrt(7) - sqrt(2) Step 3: Multiply the denominators using the difference of squares formula (a+b)(a-b) = a^2 - b^2. (sqrt(7) + sqrt(2))(sqrt(7) - sqrt(2)) = (sqrt(7))^2 - (sqrt(2))^2 = 7 - 2 = 5 Step 4: Combine the simplified numerator and denominator. sqrt(7) - sqrt(2)5 The simplified expression is: sqrt(7) - sqrt(2)5 Last free one today — make it count tomorrow, or type /upgrade for unlimited.